Finite Group Databasebeta

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C₇×#912 #10621309

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3,4,5,6,7)(8,9,10)(12,17)(13,20)(14,23)(16,24)(19,26)(21,22);(11,13)(12,16)(14,20)(15,22)(17,19)(18,26)(21,23)(24,25);(9,10)(11,12)(13,19)(14,18)(15,17)(16,22)(20,24)(21,26)(23,25)

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 891);