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C₂²×#1393449 #72321616

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

Aliases

Subgroups

882680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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