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C₄×#2264 #512763

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

Aliases

Subgroups

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 68 points:

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

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(512, 419959);