Finite Group Databasebeta

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C₄×#889 #73622

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3)(9,13)(12,15)(16,18,19,22)(17,20,21,23);(8,10,11,14)(9,12,13,15)(18,22)(20,23);(2,3)(8,9)(10,12)(11,13)(14,15)(16,17,19,21)(18,20,22,23);(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, 6198);