Finite Group Databasebeta

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C₂×#612904 #72296222

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

Aliases

Subgroups

424109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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