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C₂²×#612460 #72321315

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

Aliases

Subgroups

1030644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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), (9,10,11,12)(13,14,15,16), (13,14)(15,16)(17,18,21,23)(19,20,22,24), (5,6,7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)(23,24), (1,2)(3,4), (5,6)(7,8), (17,20)(18,22)(19,23)(21,24));