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C₂×#5220 #84041

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 17 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16617);