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C₂×#12877 #493924

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

Aliases

Subgroups

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401120);