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C₂×#1420 #13624

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

Aliases

Subgroups

143 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6612);