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C₂×#13520 #499446

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

Aliases

Subgroups

556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406642);