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C₂×#7682631 #72298868

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

Aliases

Subgroups

129099 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

220 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)(8,10)(11,12)(13,17)(14,15)(16,18), (4,6)(7,8)(9,10)(13,18)(16,17), (4,6)(11,12)(13,16)(14,15)(17,18), (4,6)(12,15)(13,18), (3,4)(5,6)(11,12)(13,17)(14,15)(16,18), (3,4)(5,6)(11,13)(12,16)(14,18)(15,17), (1,2));