Finite Group Databasebeta

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C₇×#926 #10621323

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 22 points:

(1,2,3,4,5,6,7)(8,9,10)(16,20)(19,22);(15,17,18,21)(16,19,20,22);(9,10)(11,12,13,14)(15,16)(17,19)(18,20)(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, 905);