Finite Group Databasebeta

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C₂×#5597 #85925

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1640 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)(10,12)(11,15)(13,17)(14,16);(1,2)(7,9)(10,12)(11,14)(13,17)(15,16);(12,17)(14,15);(4,5)(10,11,13,16)(12,14,17,15);(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, 18501);