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 ⋊ #28499 |
1004 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)(58,62,63,74,65,73,64,60)(59,68,69,66,70,71,79,82)(61,76,77,87,78,88,80,72)(67,83,84,81,85,86,75,89);(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)(55,57)(58,61)(59,67)(60,72)(62,76)(63,77)(64,80)(65,78)(66,81)(68,83)(69,84)(70,85)(71,86)(73,88)(74,87)(75,79)(82,89);(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)(58,60,63,62,65,74,64,73)(59,66,69,71,70,82,79,68)(61,72,77,76,78,87,80,88)(67,81,84,86,85,89,75,83);(58,59,64,69,65,70,63,79)(60,71,73,82,74,68,62,66)(61,75,77,85,78,84,80,67)(72,81,76,83,87,89,88,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=eg,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,d^b=dh,i^b=i^52,f^c=fh,i^c=i^52,i^d=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 261444);