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C₂×#13468 #499307

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

Aliases

Subgroups

754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406503);