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C₂³×#3532 #72236677

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

Aliases

Subgroups

631301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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