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C₂³×#62983 #72301673

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

Aliases

Subgroups

9727568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 9 generators on 22 points:

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

Conjugacy classes & character table

680 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), (1,2)(3,4)(5,6), (7,8,11,13)(9,12,14,10)(15,16,18,21)(17,20,22,19), (7,9)(8,10)(11,14)(12,13)(15,17,18,22)(16,19,21,20), (7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,22)(19,21), (7,9,11,14)(8,12,13,10), (7,9)(8,10)(11,14)(12,13), (7,10)(8,9)(11,12)(13,14)(15,16)(17,19)(18,21)(20,22));