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C₂×#12685 #493344

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

Aliases

Subgroups

3146 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)(5,17,21,45,19,33,51,41,20,38,28,56,25,11,31,34)(6,12,23,36,22,35,52,61,24,37,54,63,26,39,55,64)(18,46,49,66,50,32,58,60,48,44,53,65,47,59,57,62);(3,5)(4,11)(6,18)(7,25)(8,28)(9,19)(10,20)(12,32)(13,38)(14,41)(15,17)(16,33)(21,30)(22,50)(23,53)(24,48)(26,47)(27,51)(29,31)(34,43)(35,44)(36,62)(37,59)(39,46)(40,45)(42,56)(49,54)(52,57)(55,58)(60,63)(61,66)(64,65);(3,6)(4,12)(5,18)(7,26)(8,23)(9,22)(10,24)(11,32)(13,39)(14,36)(15,35)(16,37)(17,44)(19,50)(20,48)(21,49)(25,47)(27,55)(28,53)(29,52)(30,54)(31,57)(33,59)(34,60)(38,46)(40,64)(41,62)(42,61)(43,63)(45,65)(51,58)(56,66)

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, 400540);