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C₂³×#2679 #72267186

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

Aliases

Subgroups

373141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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