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C₂×#12617 #492981

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

Aliases

Subgroups

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400177);