Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1381 ⋊ C2 |
| Sylow | C53 ⋊ #13072 |
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 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)(58,61)(59,65)(60,70)(62,67)(63,68)(64,75)(66,73)(69,71)(72,83)(74,80)(76,79)(77,85)(78,89)(81,84)(82,86)(87,88);(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)(54,56,57,55)(58,60,62,77,64,72,79,82,65,73,80,71,63,81,78,88)(59,66,74,69,68,84,89,87,61,70,67,85,75,83,76,86);(54,55,57,56)(58,59,63,68,65,61,64,75)(60,69,72,86,73,85,81,87)(62,76,78,74,80,89,79,67)(66,82,83,71,70,88,84,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87002);