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C₂³×#2342 #72295987

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

Aliases

Subgroups

252757 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

400 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((12,14)(15,16,19,18)(17,20,21,22), (11,12)(13,14), (15,17)(16,20)(18,22)(19,21), (7,8,9,10)(15,18,19,16)(17,20,21,22), (3,4), (5,6), (1,2)(3,4)(5,6));