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C₂³×#1440 #72325510

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

Aliases

Subgroups

235061 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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