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#62979

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

No aliases for this group.

Subgroups

3055 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 64 points:

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

Polycyclic presentation:

2^8|a^2=h,b^2=g,c^2=g,d^2=h,e^2=g,b^a=bg,c^a=ch,d^a=dh,f^a=fg,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=eh

Conjugacy classes & character table

67 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55967);