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C₂³×#37644 #72289495

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

Aliases

Subgroups

4247576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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((7,8,9,10)(11,12,13,14)(15,16,19,21)(17,18,22,20), (11,12)(13,14)(15,17)(16,18)(19,22)(20,21), (11,12,13,14)(15,17,19,22)(16,20,21,18), (7,8)(9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22), (7,8)(9,10)(15,17)(16,18)(19,22)(20,21), (3,4), (5,6), (1,2)(3,4)(5,6));