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C₂²×#35840 #72292909

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

Aliases

Subgroups

99221 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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), (9,10,12,13)(11,14,15,16)(17,18,20,22)(19,21,24,23), (6,8)(10,13)(11,15)(17,18)(19,23)(20,22)(21,24), (9,11,12,15)(10,14,13,16)(17,19)(18,21)(20,24)(22,23), (5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,19)(18,21)(20,24)(22,23), (9,11)(10,14)(12,15)(13,16), (1,2)(3,4));