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C₂²×#42998 #72292905

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

Aliases

Subgroups

116197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((3,4), (5,6)(7,8)(10,13)(14,16)(17,18,21,22)(19,23,24,20), (5,6)(7,8)(17,18)(19,20)(21,22)(23,24), (5,6,7,8)(11,15)(14,16)(19,24)(20,23), (5,6)(7,8)(9,10,12,13)(11,16,15,14)(17,19,21,24)(18,20,22,23), (9,11)(10,14)(12,15)(13,16)(17,20)(18,19)(21,23)(22,24), (1,2)(3,4));