Finite Group Databasebeta

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C₂²×#47929 #72278714

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

Aliases

Subgroups

121393 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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