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C₂²×#47827 #72278478

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

Aliases

Subgroups

136425 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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