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C₂×#7548 #153577

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

Aliases

Subgroups

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 66 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60773);