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C₂×M₁₂₈ #13736

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

Aliases

Subgroups

67 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6724);