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C₂×Dic₄₉ #87626

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 55 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 6);