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C₂²×#2306470 #72297004

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

Aliases

Subgroups

713252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

320 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((10,12)(13,14)(15,16)(18,19)(22,23), (10,12)(14,15)(17,18)(19,21)(20,23)(22,24), (5,6)(7,8)(9,10,11,12)(13,14,16,15)(18,19)(20,24), (6,7)(9,10,11,12)(13,14,16,15)(17,19,21,18)(20,23,24,22), (5,7,8,6)(9,10)(11,12)(13,15,16,14)(17,20,21,24)(18,22,19,23), (3,4), (1,2)(3,4));