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C₂²×#2805719 #72291917

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

Aliases

Subgroups

836140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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