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C₂×#5653 #86005

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 17 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18581);