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C₂×Dic₅₀ #87741

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

57 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 35);