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C₂×SD₁₂₈ #13739

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

67 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 66 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6727);