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C₂×#12840 #493821

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

Aliases

Subgroups

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401017);