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C₂×#648350 #72331127

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

Aliases

Subgroups

71345 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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