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C₂×#2262 #33978

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

Aliases

Subgroups

235 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26966);