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C₂²×#11014 #72314724

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

Aliases

Subgroups

46877 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 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((5,6)(7,8)(9,10)(11,15)(12,14)(13,17)(16,21)(18,22)(19,23)(20,24), (5,6)(7,8)(10,14)(11,18)(12,21)(16,17)(19,20)(22,23), (6,8)(9,11,12,18,13,20,21,19)(10,15,14,22,17,24,16,23), (1,2), (3,4));