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#27295283

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

272 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 117 points:

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

Polycyclic presentation:

2^8,53|a^2=e,b^2=h,c^2=gh,d^2=g,e^2=f,f^2=h,b^a=bd,c^a=cf,d^a=df,g^a=gh,i^a=i^52,d^b=dg,e^b=efgh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,e^d=eh

Conjugacy classes & character table

866 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 80759);