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C₂³×#35250 #72324544

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

Aliases

Subgroups

5888120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 22 points:

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

Conjugacy classes & character table

512 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)(15,16,20,21)(17,19,18,22), (11,12)(13,14)(15,17)(16,19)(18,20)(21,22), (3,4), (5,6), (16,21)(17,18), (1,2)(3,4)(5,6), (8,10)(11,12,13,14)(15,18,20,17)(16,22,21,19), (7,8)(9,10)(11,12)(13,14)(15,19,20,22)(16,18,21,17));