Finite Group Databasebeta

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C₇×#803 #10620601

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 183);