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C₂×#12542 #492833

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

Aliases

Subgroups

852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400029);