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C₂×#651179 #72325417

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

Aliases

Subgroups

48101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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