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C₂×#12744 #493540

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

Aliases

Subgroups

3104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400736);