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C₂×#7630944 #72240964

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

Aliases

Subgroups

204157 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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