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C₂³×#2539 #72289382

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

Aliases

Subgroups

290357 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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)(15,16,19,20)(17,21,22,18), (3,4), (11,12,13,14)(16,20)(18,21), (7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(19,22)(20,21), (7,8)(9,10)(11,12)(13,14)(15,18)(16,17)(19,21)(20,22), (5,6), (1,2)(3,4)(5,6));