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C₂×#14004 #514297

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

Aliases

Subgroups

7258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421493);