Finite Group Databasebeta

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C₂×#616177 #72299460

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

Aliases

Subgroups

116421 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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