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C₂×#12979 #494409

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

Aliases

Subgroups

1272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401605);