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C₂²×#34992 #72289151

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

Aliases

Subgroups

220685 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(10,13)(11,15)(19,23)(21,24), (5,6)(7,8)(11,15)(14,16)(17,18,20,22)(19,24,23,21), (9,10)(11,14)(12,13)(15,16)(17,19)(18,21)(20,23)(22,24), (3,4), (17,19)(18,21)(20,23)(22,24), (9,11)(10,14)(12,15)(13,16)(17,19)(18,21)(20,23)(22,24), (1,2)(3,4));