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C₂²×#16363 #72337040

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

Aliases

Subgroups

82701 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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