Finite Group Databasebeta

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C₃×D₄₉ #64415

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 4);