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C₂×#13558 #512556

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

Aliases

Subgroups

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419752);