Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1827 ⋊ C2 |
| Sylow | C53 ⋊ #24985 |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,58,59,71,61,70,60,56)(55,64,65,62,67,68,66,79)(57,74,75,85,77,73,76,69)(63,81,72,78,82,80,83,84);(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)(54,57)(55,63)(56,69)(58,74)(59,75)(60,76)(61,77)(62,78)(64,81)(65,72)(66,83)(67,82)(68,80)(70,73)(71,85)(79,84);(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)(54,56,60,70,61,71,59,58)(55,62,66,64,67,79,65,68)(57,73,75,69,77,74,76,85)(63,80,72,84,82,81,83,78);(54,55)(56,68)(57,72)(58,62)(59,66)(60,65)(61,67)(63,75)(64,71)(69,84)(70,79)(73,81)(74,80)(76,82)(77,83)(78,85)Polycyclic presentation:
2^8,53|b^2=f,d^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,i^b=i^52,f^c=fh,g^c=gh,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, 214655);