Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1951 ⋊ C2 |
| Sylow | C53 ⋊ #12952 |
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,56)(55,61)(57,70)(58,74)(59,66)(60,75)(62,80)(63,76)(64,82)(65,83)(67,72)(68,84)(69,78)(71,85)(73,79)(77,81);(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)(54,55,58,73,59,63,72,64)(56,61,74,79,66,76,67,82)(57,69,68,60,71,81,83,62)(65,80,70,78,84,75,85,77);(55,60,63,62)(56,65,66,84)(57,68)(58,72)(61,76)(64,81,73,69)(67,70,74,85)(71,83)(75,77)(78,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=fg,d^2=g,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,d^b=dg,e^b=egh,f^b=fh,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,f^c=fh,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86278);