Finite Group Databasebeta

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C₂×#612517 #72298689

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

Aliases

Subgroups

76411 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(8,10)(12,14)(16,19)(17,21), (4,6)(8,10)(11,12)(13,14)(15,16)(17,22)(18,19)(20,21), (3,4,5,6)(7,8,9,10)(16,19)(17,21), (4,6)(7,8,9,10)(15,16)(17,22)(18,19)(20,21), (3,4)(5,6)(7,8)(9,10)(15,17)(16,20)(18,21)(19,22), (1,2));