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D₇×Q₃₂ #89689

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 39 points:

(1,3,6,14)(2,7,10,24)(4,16,19,32)(5,21,17,13)(8,26,27,31)(9,28,20,23)(11,29,30,15)(12,25,22,18)(33,34,36,38,39,37,35);(1,2,6,10)(3,11,14,30)(4,15,19,29)(5,20,17,9)(7,22,24,12)(8,25,27,18)(13,31,21,26)(16,28,32,23);(34,35)(36,37)(38,39)

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 451);