Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1412 ⋊ C2 |
| Sylow | C53 ⋊ #13609 |
348 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 57 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)(54,57)(55,61)(56,66)(58,71)(59,70)(60,74)(62,79)(63,77)(64,78)(65,80)(67,81)(68,69)(72,83)(73,84)(75,82)(76,85);(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)(54,56)(55,60)(57,69)(58,72)(59,68)(61,74)(62,75)(63,65)(64,76)(66,70)(67,73)(71,81)(77,80)(78,85)(79,82)(83,84);(54,55)(56,65,67,60)(57,61)(58,63,73,62)(59,64)(66,80,81,74)(68,75,72,76)(69,82,83,85)(70,78)(71,77,84,79)Polycyclic presentation:
2^8,53|a^2=e,d^2=gh,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,c^b=cg,d^b=dgh,e^b=efg,f^b=fh,i^b=i^52,d^c=dh,i^c=i^52,e^d=egh,f^e=fh389 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89973);