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C₂²×#36704 #72324715

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

Aliases

Subgroups

116445 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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