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C₂×#13499 #499397

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

Aliases

Subgroups

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406593);