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C₂³×#2673 #72289457

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

Aliases

Subgroups

186045 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

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