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C₂²×#1393451 #72321608

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

Aliases

Subgroups

769352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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