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C₂²×#42475 #72278747

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

Aliases

Subgroups

136221 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

GAP

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

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