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C₂²×#52008 #72233985

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

Aliases

Subgroups

112553 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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