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C₂³×#2321 #72289481

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

Aliases

Subgroups

257925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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