FiSGO.SimpleGroups

Module implementing simple group objects.

Functions

char_check	Helper function to check if a hiss-malle representation exists in a given characteristic.
code_normalizer	Given a simple group code, returns a normalized version of the code.
hiss_malle_data	Interface to the compressed JSON file Hiss_Malle_data.json.bz2.
hiss_malle_lookup	A function to browse the file containing data on representations of degree less than 250, compiled by Gerard Hiss and Gunter Malle in [HM1] and [HM2].
lubeck_data	Interface to the compressed JSON files Lubeck_[code].json.bz2.
lubeck_exceptional_data	Interface to the JSON file Lubeck_exceptional_mult.json.
modularity_group	Auxiliary function to find the modularity class of some group in Lübeck's data.
simple_group	Given a simple group code, returns a derived object of SimpleGroup corresponding to the provided code.
simple_group_ids	Returns a dictionary relating simple group IDs and their classes.
sporadic_group_ids	Returns a list with all sporadic simple group IDs.
sporadic_groups_data	Interface to the compressed JSON file sporadic_grous_data.json.bz2.
sporadic_lookup_property	Helper function to look up a property of a sporadic group in the JSON file.

Classes

Alternating	Class representing the Alternating group \(\mathrm{A}_n\), a simple group when n > 4.
BiParamSimpleGroup	Base class for simple groups with two parameters.
ChevalleyA	Class representing the classical Chevalley group \(A_n(q)\), a simple group of Lie type.
ChevalleyB	Class representing the classical Chevalley group \(B_n(q)\), a simple group of Lie type.
ChevalleyC	Class representing the classical Chevalley group \(C_n(q)\), a simple group of Lie type.
ChevalleyD	Class representing the classical Chevalley group \(D_n(q)\), a simple group of Lie type.
Cyclic	Class representing the Cyclic group \(\mathrm{C}_n\), a simple group when n is prime.
ExcetionalChevalleyE6	Class representing the exceptional Chevalley group \(E_6(q)\), a simple group of Lie type.
ExcetionalChevalleyE7	Class representing the exceptional Chevalley group \(E_7(q)\), a simple group of Lie type.
ExcetionalChevalleyE8	Class representing the exceptional Chevalley group \(E_8(q)\), a simple group of Lie type.
ExcetionalChevalleyF4	Class representing the exceptional Chevalley group \(F_4(q)\), a simple group of Lie type.
ExcetionalChevalleyG2	Class representing the exceptional Chevalley group \(G_2(q)\), a simple group of Lie type.
ExcetionalSteinberg2E6	Class representing the exceptional Steinberg group \({}^2E_6(q^2)\), a simple group of Lie type.
ExcetionalSteinberg3D4	Class representing the exceptional Steinberg group \({}^3D_4(q^3)\), a simple group of Lie type.
Ree2F4	Class representing the Ree group \({}^2F_4(2^{2n+1})\), a simple group of Lie type.
Ree2G2	Class representing the Ree group \({}^2G_2(3^{2n+1})\), a simple group of Lie type.
SimpleGroup	Base class for simple groups.
Sporadic	Class representing the Sporadic simple groups.
Steinberg2A	Class representing the classical Steinberg group \({}^2A_n(q^2)\), a simple group of Lie type.
Steinberg2D	Class representing the classical Steinberg group \({}^2D_n(q^2)\), a simple group of Lie type.
Suzuki	Class representing the Suzuki group \({}^2B_2(2^{2n+1})\), a simple group of Lie type.
Tits	Class representing the Tits group \({}^2F_4(2)'\), a simple group of Lie type.
UniParamSimpleGroup	Base class for simple groups with one parameter.