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C₂×#13216 #495143

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

Aliases

Subgroups

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402339);