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C₂×#1258521 #72295107

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

Aliases

Subgroups

74423 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((7,8)(9,10)(11,12,13,14)(15,16,20,22)(17,19,21,18), (11,12)(13,14)(15,17,20,21)(16,19,22,18), (4,6)(8,10)(11,12)(13,14)(15,18,20,19)(16,21,22,17), (3,4)(5,6)(7,8)(9,10)(11,12,13,14)(15,19,20,18)(16,21,22,17), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,21)(20,22), (1,2));