Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1886 ⋊ C2 |
| Sylow | C53 ⋊ #22892 |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,62)(59,68)(60,73)(61,76)(63,81)(64,79)(65,80)(66,82)(67,83)(69,87)(70,85)(71,86)(72,88)(74,89)(75,84)(77,78);(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)(58,61,65,60)(59,67,71,66)(62,76,80,73)(63,77,64,74)(68,83,86,82)(69,75,70,72)(78,79,89,81)(84,85,88,87);(54,56,57,55)(58,60,65,61)(59,66,71,67)(62,78,80,89)(63,77,64,74)(68,84,86,88)(69,75,70,72)(73,81,76,79)(82,87,83,85);(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)(54,55,57,56)(58,59,65,71)(60,72,61,75)(62,68,80,86)(63,70,64,69)(66,77,67,74)(73,88,76,84)(78,83,89,82)(79,87,81,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=de,e^b=eh,f^c=fh,i^c=i^52,e^d=eh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 190383);