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C₂×#647938 #72251007

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

Aliases

Subgroups

78549 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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