Finite Group Databasebeta

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C₄²×Dic₇ #89702

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 464);