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C₂²×#47942 #72236673

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

Aliases

Subgroups

125777 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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