Finite Group Databasebeta

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C₇×#23882 #13201098

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16870);