Finite Group Databasebeta

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C₂²×#34194 #72300999

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

Aliases

Subgroups

114725 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((5,6,7,8)(11,15)(13,16)(18,22)(20,23), (17,18)(19,23)(20,24)(21,22), (9,10,12,14)(11,13,15,16)(17,19,21,24)(18,23,22,20), (9,10)(11,13)(12,14)(15,16), (9,11,12,15)(10,13,14,16)(17,20,21,23)(18,24,22,19), (3,4), (1,2)(3,4));