Finite Group Databasebeta

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C₂×#674138 #72323276

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

Aliases

Subgroups

78277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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