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C₂×#13335 #498871

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

Aliases

Subgroups

1528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406067);