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#7627682

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

Aliases

No aliases for this group.

Subgroups

5890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 68 points:

(1,2,3,4)(5,6,10,11)(7,15,18,12)(8,13,19,24)(9,22,23,14)(16,27,20,25)(17,26,31,29)(21,34,32,28)(30,35,33,36)(37,38,44,41)(39,48,40,45)(42,46,56,53)(43,54,57,47)(49,60,51,58)(50,59,52,62)(55,65,66,61)(63,67,64,68);(6,11)(8,19)(9,23)(12,15)(16,20)(17,31)(28,34)(35,36)(37,39,44,40)(38,45,41,48)(42,51,56,49)(43,50,57,52)(46,60,53,58)(47,59,54,62)(55,64,66,63)(61,68,65,67);(5,7,10,18)(6,12,11,15)(8,20,19,16)(9,17,23,31)(13,27,24,25)(14,26,22,29)(21,33,32,30)(28,36,34,35)(37,40,44,39)(38,45,41,48)(42,51,56,49)(43,52,57,50)(46,58,53,60)(47,59,54,62)(55,64,66,63)(61,67,65,68);(5,6)(7,15)(8,13)(9,14)(10,11)(12,18)(16,27)(17,29)(19,24)(20,25)(21,28)(22,23)(26,31)(30,36)(32,34)(33,35)(37,41,44,38)(39,48,40,45)(42,53,56,46)(43,54,57,47)(49,60,51,58)(50,62,52,59)(55,65,66,61)(63,68,64,67);(5,8)(6,13)(7,16)(9,21)(10,19)(11,24)(12,25)(14,28)(15,27)(17,30)(18,20)(22,34)(23,32)(26,35)(29,36)(31,33)(37,42)(38,46)(39,49)(40,51)(41,53)(43,55)(44,56)(45,58)(47,61)(48,60)(50,63)(52,64)(54,65)(57,66)(59,67)(62,68);(5,9,10,23)(6,14,11,22)(7,17,18,31)(8,21,19,32)(12,26,15,29)(13,28,24,34)(16,30,20,33)(25,35,27,36)(37,43)(38,47)(39,50)(40,52)(41,54)(42,55)(44,57)(45,59)(46,61)(48,62)(49,63)(51,64)(53,65)(56,66)(58,67)(60,68)

Polycyclic presentation:

2^9|a^2=i,b^2=gh,c^2=g,d^2=gh,f^2=h,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

134 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7534878);