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C₂×#13312 #498801

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

Aliases

Subgroups

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 405997);