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C₂×#649101 #72277976

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

Aliases

Subgroups

90899 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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