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C₂×#13418 #499090

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

Aliases

Subgroups

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406286);