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C₂³×#34980 #72289148

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

Aliases

Subgroups

9514584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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