Finite Group Databasebeta

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C₂×#648355 #72320412

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

Aliases

Subgroups

80337 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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