Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1966 ⋊ C2 |
| Sylow | C53 ⋊ #28498 |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
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)(58,62,65,74,64,73,63,60)(59,68,70,66,71,83,69,81)(61,77,79,76,80,88,78,72)(67,85,87,82,86,89,75,84);(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)(55,57)(58,61)(59,67)(60,72)(62,77)(63,78)(64,80)(65,79)(66,82)(68,85)(69,75)(70,87)(71,86)(73,88)(74,76)(81,84)(83,89);(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)(54,55,56,57)(58,60,63,73,64,74,65,62)(59,66,69,68,71,81,70,83)(61,76,78,77,80,72,79,88)(67,84,75,89,86,82,87,85);(58,59,65,69,64,71,63,70)(60,68,62,81,74,83,73,66)(61,75,78,67,80,87,79,86)(72,84,88,85,76,82,77,89)Polycyclic presentation:
2^8,53|a^2=fh,b^2=egh,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,i^b=i^52,f^c=fh,i^c=i^52,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 261435);