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C₂×#7696413 #72278293

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

Aliases

Subgroups

129485 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

214 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((3,4)(5,6)(11,12)(13,17)(14,16)(15,18), (3,4,5,6)(11,12,14,16)(13,15,18,17), (7,8,9,10)(11,12)(13,15)(14,16)(17,18), (7,8)(9,10)(11,13,14,18)(12,15,16,17), (3,4,5,6)(7,8,9,10), (3,4)(5,6)(7,8)(9,10), (1,2));