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C₂×#33442 #7622584

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

Aliases

Subgroups

1904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,8,14,9,13,28,38,10,15,29,39,7,25,27,51)(5,16,19,41,18,11,30,32,20,33,45,57,26,34,52,58)(6,12,23,37,24,36,50,60,21,35,46,59,22,47,49,63)(17,40,44,61,43,31,53,55,42,56,62,66,48,54,64,65);(3,5)(4,11)(6,17)(7,26)(8,19)(9,18)(10,20)(12,31)(13,33)(14,32)(15,34)(16,25)(21,42)(22,48)(23,44)(24,43)(27,52)(28,30)(29,45)(35,54)(36,56)(37,55)(38,57)(39,58)(40,47)(41,51)(46,62)(49,64)(50,53)(59,65)(60,66)(61,63);(3,6,8,23,9,24,28,50,10,21,29,46,7,22,27,49)(4,12,14,37,13,36,38,60,15,35,39,59,25,47,51,63)(5,17,19,44,18,43,30,53,20,42,45,62,26,48,52,64)(11,31,32,55,33,56,57,66,34,54,58,65,16,40,41,61);(6,21)(12,35)(17,42)(22,24)(23,46)(31,54)(36,47)(37,59)(40,56)(43,48)(44,62)(49,50)(53,64)(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, 7529780);