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D₃×Q₆₄ #69382

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 67 points:

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 1958);