Finite Group Databasebeta

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C₄×#950 #82505

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

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, 15081);