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C₂×Dic₅₂ #88159

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 126);