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C₂×#648354 #72298663

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

Aliases

Subgroups

75853 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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