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C₂×#12885 #494075

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

Aliases

Subgroups

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401271);