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C₂²×#634 #64355

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1003);