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C₂×C₂₇⋊C₈ #88362

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2)(3,4,5,7,6,8,9,10)(12,15)(13,19)(14,22)(16,17)(18,28)(20,21)(23,30)(24,29)(25,35)(26,34)(27,33)(31,32)(36,37);(1,2)(11,30,24,31,35,33,13,12,34,14,37,28,20,17,16,21,18,36,22,26,15,19,27,25,32,29,23)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 9);