FiSGO.SimpleGroups.simple_group_ids

simple_group_ids()

Returns a dictionary relating simple group IDs and their classes. IDs are the first two characters of a simple group code and serve to identify the family of simple groups. We list the IDs and the corresponding groups and number of parameters.

Group notations taken from Wikipedia.

• Zero-parametric

  • “TT”: Tits group \({}^2F_4(2)'\)

• Uniparametric

  • “CY”: Simple cyclic groups \(\mathrm{C}_n\)

  • “AA”: Alternating groups \(\mathrm{A}_n\)

  • “E6”: Exceptional Chevalley groups \(E_6(q)\)

  • “E7”: Exceptional Chevalley groups \(E_7(q)\)

  • “E8”: Exceptional Chevalley groups \(E_8(q)\)

  • “F4”: Exceptional Chevalley groups \(F_4(q)\)

  • “G2”: Exceptional Chevalley groups \(G_2(q)\)

  • “2E”: Exceptional Steinberg groups \({}^2E_6(q^2)\)

  • “3D”: Exceptional Steinberg groups \({}^3D_4(q^3)\)

  • “SZ”: Suzuki groups \({}^2B_2(2^{2n+1})\)

  • “RF”: Ree groups \({}^2F_4(2^{2n+1})\)

  • “RG”: Ree groups \({}^2G_2(3^{2n+1})\)

• Biparametric

  • “CA”: Classical Chevalley groups \(A_n(q)\)

  • “CB”: Classical Chevalley groups \(B_n(q)\)

  • “CC”: Classical Chevalley groups \(C_n(q)\)

  • “CD”: Classical Chevalley groups \(D_n(q)\)

  • “SA”: Classical Steinberg groups \({}^2A_n(q^2)\)

  • “SD”: Classical Steinberg groups \({}^2D_n(q^2)\)

Caution

The Fischer 24’ group should be written as r"SP-Fi24'" for proper handling of the ‘ character.

Returns:

A dictionary relating group IDs and their classes.