Finite Group Databasebeta

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C₂²×#13424 #72284708

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

Aliases

Subgroups

13497 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

124 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((1,2)(3,4)(6,8)(10,14)(15,22)(16,24)(17,23), (1,2)(3,4)(5,6)(7,8)(10,15,16,17)(12,20)(14,22,24,23)(18,21), (5,6)(7,8)(9,10,12,14)(11,17,18,23)(13,16,20,24)(15,21,22,19), (1,2), (3,4));