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#27186911

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 121 points:

(1,2,7,3)(4,6,17,13)(5,8,15,9)(10,12,31,27)(11,18,25,19)(14,16,29,23)(20,22,49,41)(21,32,39,33)(24,30,45,37)(26,28,47,43)(34,36,52,54)(35,50,57,51)(38,48,61,55)(40,42,67,63)(44,46,65,59)(53,69,72,58)(56,68,75,70)(60,66,79,73)(62,64,81,77)(71,83,86,76)(74,82,89,84)(78,80,91,87)(85,93,96,90)(88,92,98,94)(95,99,100,97)(106,108,110,118,111,116,109,117)(107,113,114,120,115,121,112,119);(2,4,5,3)(6,10,11,9)(7,8,14,13)(12,20,21,19)(15,18,24,23)(16,26,27,17)(22,34,35,33)(25,32,38,37)(28,40,41,31)(29,30,44,43)(36,52,53,51)(39,50,56,55)(42,58,54,49)(45,48,60,59)(46,62,63,47)(57,69,71,70)(61,68,74,73)(64,76,72,67)(65,66,78,77)(75,83,85,84)(79,82,88,87)(80,90,86,81)(89,93,95,94)(91,92,97,96)(98,99,101,100)(102,103,104,105)(107,112,115,114)(108,116)(113,120,121,119)(117,118);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,54,58)(45,59,60,48)(46,47,63,62)(57,70,71,69)(61,73,74,68)(64,67,72,76)(65,77,78,66)(75,84,85,83)(79,87,88,82)(80,81,86,90)(89,94,95,93)(91,96,97,92)(98,100,101,99)(106,107,110,114,111,115,109,112)(108,113,118,120,116,121,117,119)

Polycyclic presentation:

2^7,101|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^10,c^b=cg,h^b=h^91,h^c=h^10,h^e=h^100,h^f=h^100

Conjugacy classes & character table

394 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 20289);