Finite Group Databasebeta

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C₂×#687655 #72296409

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

Aliases

Subgroups

78691 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)(18,21)(19,22);(4,6)(8,10)(12,14)(15,17,18,22)(16,19,21,20);(11,12)(13,14)(15,17)(16,20)(18,22)(19,21);(15,17)(16,19)(18,22)(20,21);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,20)(18,21)(19,22);(1,2)

Conjugacy classes & character table

184 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)(18,21)(19,22), (4,6)(8,10)(12,14)(15,17,18,22)(16,19,21,20), (11,12)(13,14)(15,17)(16,20)(18,22)(19,21), (15,17)(16,19)(18,22)(20,21), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,20)(18,21)(19,22), (1,2));