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C₂×#13078 #494669

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

Aliases

Subgroups

1266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401865);