Finite Group Databasebeta

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C₂×#517411 #72256558

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

Aliases

Subgroups

430997 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((15,16)(17,21)(18,22)(19,20), (11,12)(13,14), (4,6)(7,8,9,10)(12,14)(16,20)(18,21), (11,12)(13,14)(15,17)(16,21)(18,20)(19,22), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,18,19,21)(16,22,20,17));