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C₂×#33981 #7625190

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

Aliases

Subgroups

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532386);