Finite Group Databasebeta

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C₂²×#6342373 #72314360

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

Aliases

Subgroups

8286648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

608 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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