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C₂×D₇×Q₁₆ #90454

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

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

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, 1216);