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C₂×#12597 #492929

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

Aliases

Subgroups

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400125);