Finite Group Databasebeta

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C₂³×#14715 #72289538

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

Aliases

Subgroups

9227624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

512 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((3,4), (8,10)(12,14)(15,16,17,18), (11,12)(13,14)(19,20,21,22), (15,16)(17,18)(19,20)(21,22), (7,8)(9,10)(11,12)(13,14)(15,16)(17,18), (5,6), (1,2)(3,4)(5,6));