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C₂×#36097 #7629720

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

Aliases

Subgroups

13750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536916);