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C₂×#12830 #493799

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

Aliases

Subgroups

1018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400995);