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C₂×#33441 #7622583

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

Aliases

Subgroups

1916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529779);