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C₂×#12832 #493804

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

Aliases

Subgroups

944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401000);