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C₂×Dic₄₈ #69370

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 69 points:

(3,4,5)(6,8,19,45,10,21,46,62,29,51,65,63,39,60,27,32,12,23,36,61,30,52,26,49,11,22,47,68,25,48,9,20)(7,13,24,42,15,33,54,53,31,59,57,69,58,66,38,44,17,35,56,67,40,64,37,43,16,34,55,50,28,41,14,18);(1,2)(4,5)(6,7,12,17)(8,18,23,44)(9,24,27,56)(10,28,30,58)(11,31,29,16)(13,32,35,20)(14,36,38,19)(15,39,40,25)(21,50,52,69)(22,53,51,43)(26,57,46,55)(33,63,64,68)(34,49,59,62)(37,47,54,65)(41,61,66,45)(42,60,67,48);(1,2)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 1946);