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C₂×#612443 #72286770

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

Aliases

Subgroups

165705 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((4,6)(8,10)(12,14)(15,16,19,20)(17,18,21,22), (3,4,5,6)(7,8,9,10)(15,17,19,21)(16,18,20,22), (11,12,13,14)(15,17)(16,18)(19,21)(20,22), (1,2), (7,8)(9,10), (3,4)(5,6)(7,8)(9,10)(15,18)(16,17)(19,22)(20,21));