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C₂⁴×D₄⋊C₈ #72286583

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

Aliases

Subgroups

69077 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

448 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((1,2), (3,4), (9,10)(11,13)(12,15)(14,16)(17,18)(19,20)(21,23)(22,24), (10,13)(11,16)(14,15)(17,19,20,23,21,22,24,18), (5,6), (7,8));