Finite Group Databasebeta

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D₇×#126 #90394

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1156);