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C₂²×#47928 #72292893

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

Aliases

Subgroups

115729 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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