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C₂²×#62852 #72279148

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

841421 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

(6,7)(9,10)(11,12)(13,15)(14,17)(16,19)(18,20)(21,24)(22,23);(5,6,8,7)(9,11)(10,12)(13,16)(14,22)(15,19)(17,23)(18,24)(20,21);(6,7)(9,12,15,16)(10,11,13,19)(14,23,24,20)(17,22,21,18);(5,7,8,6)(9,13,15,10)(11,16,19,12)(14,21,24,17)(18,23,22,20);(9,11)(10,16)(12,13)(14,18)(15,19)(17,23)(20,21)(22,24);(9,14)(10,17)(11,18)(12,20)(13,21)(15,24)(16,23)(19,22);(3,4);(1,2)(3,4)

Conjugacy classes & character table

328 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((6,7)(9,10)(11,12)(13,15)(14,17)(16,19)(18,20)(21,24)(22,23), (5,6,8,7)(9,11)(10,12)(13,16)(14,22)(15,19)(17,23)(18,24)(20,21), (6,7)(9,12,15,16)(10,11,13,19)(14,23,24,20)(17,22,21,18), (5,7,8,6)(9,13,15,10)(11,16,19,12)(14,21,24,17)(18,23,22,20), (9,11)(10,16)(12,13)(14,18)(15,19)(17,23)(20,21)(22,24), (9,14)(10,17)(11,18)(12,20)(13,21)(15,24)(16,23)(19,22), (3,4), (1,2)(3,4));