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C₂×#33688 #7623144

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

Aliases

Subgroups

1629 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530340);