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C₂×#7641845 #72240963

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

Aliases

Subgroups

218405 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((17,21)(19,22), (1,2), (4,6)(7,8,10,12)(9,13,14,11)(15,16,18,20)(17,22,21,19), (15,16)(17,19)(18,20)(21,22), (9,14)(11,13)(17,21)(19,22), (7,8)(9,11)(10,12)(13,14)(15,16)(17,19)(18,20)(21,22), (3,4)(5,6)(7,9)(8,11)(10,14)(12,13)(15,17)(16,19)(18,21)(20,22));