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C₂×#12893 #494093

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

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, 401289);