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C₂×Dic₃₆ #63461

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 27 points:

(3,4,7,9,11,10,5,8,6)(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20);(1,2)(4,6)(5,9)(7,8)(10,11)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22);(1,2)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 109);