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C₂×#154446 #72334588

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

Aliases

Subgroups

73657 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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