Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1497 ⋊ C2 |
| Sylow | C53 ⋊ #8490 |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2)(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)(54,57)(55,61)(56,65)(58,72)(59,69)(60,74)(62,68)(63,79)(64,80)(66,81)(67,83)(70,73)(71,82)(75,85)(76,77)(78,84)(86,89)(87,93)(88,97)(90,101)(91,102)(92,106)(94,108)(95,100)(96,110)(98,112)(99,113)(103,115)(104,116)(105,117)(107,114)(109,111);(54,56,59,66)(55,60,62,64)(57,65,69,81)(58,71,73,67)(61,74,68,80)(63,78,77,75)(70,83,72,82)(76,85,79,84)(86,88,91,99)(87,92,95,107)(89,97,102,113)(90,104,105,98)(93,106,100,114)(94,109,103,96)(101,116,117,112)(108,111,115,110);(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)(54,55,58,63,59,62,73,77)(56,64,67,78,66,60,71,75)(57,68,70,79,69,61,72,76)(65,80,82,85,81,74,83,84)(86,87)(88,96)(89,100,102,93)(90,103)(91,95)(92,98)(94,105)(97,111,113,110)(99,109)(101,108,117,115)(104,107)(106,112,114,116)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,f^c=fg,i^c=i^52869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61917);