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#62980

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

Aliases

No aliases for this group.

Subgroups

3057 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^8|a^2=h,b^2=g,d^2=gh,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, 55968);