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C₂×#33532 #7622835

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

Aliases

Subgroups

3834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530031);