Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1365 ⋊ C2 |
| Sylow | C53 ⋊ #12395 |
296 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 65 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) = 6784 |
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)(55,61)(57,58)(60,68)(62,63)(64,69)(65,66)(70,72,74,75)(71,77,78,83)(73,79,82,80)(76,81,84,85);(54,56,59,67)(55,60,63,69)(57,66,58,65)(61,68,62,64)(70,71,74,78)(72,77,75,83)(73,81,82,85)(76,79,84,80);(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)(54,55,59,63)(56,64,67,68)(57,62,58,61)(60,66,69,65)(71,76)(72,75)(73,80)(77,85)(78,84)(79,82)(81,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=gh,c^2=h,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^52,d^b=df,e^b=eg,f^b=fh,d^c=dg,e^c=eg,i^c=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83538);