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C₂²×#7966358 #72336890

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

Aliases

Subgroups

At least 10464 conjugacy classes of subgroups; only the 445696 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

Conjugacy classes & character table

404 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((17,18,21,24)(19,20,23,22), (5,6,7,8)(9,10,13,12)(11,14,16,15)(17,19,21,23)(18,22,24,20), (9,11)(10,14)(12,15)(13,16)(17,19)(18,20)(21,23)(22,24), (5,6,7,8)(9,11,13,16)(10,14,12,15)(17,18,21,24)(19,22,23,20), (3,4), (6,8)(9,11)(10,15)(12,14)(13,16)(17,19)(18,20)(21,23)(22,24), (1,2)(3,4), (5,6)(7,8)(9,12,13,10)(11,15,16,14)(17,20)(18,23)(19,24)(21,22));