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C₂×#13199 #495107

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

Aliases

Subgroups

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402303);