Finite Group Databasebeta

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C₂³×#2472 #72289464

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

Aliases

Subgroups

250301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((7,8,9,10)(12,14)(15,16,18,20)(17,21,22,19), (7,8)(9,10)(12,14), (7,8,9,10)(11,12,13,14)(15,17,18,22)(16,19,20,21), (7,8)(9,10)(15,16)(17,21)(18,20)(19,22), (3,4), (5,6), (1,2)(3,4)(5,6));