Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1335 ⋊ C2 |
| Sylow | C53 ⋊ #12046 |
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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:
(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)(54,57,58,71,60,73,76,85,61,74,66,80,59,72,75,84)(55,62,64,78,65,79,68,81,56,67,69,82,70,83,63,77);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56)(55,61)(57,67)(58,69)(59,65)(60,70)(62,74)(63,76)(64,66)(68,75)(71,82)(72,79)(73,83)(77,85)(78,80)(81,84);(54,55,58,64,60,65,76,68,61,56,66,69,59,70,75,63)(57,62,71,78,73,79,85,81,74,67,80,82,72,83,84,77)Polycyclic presentation:
2^8,53|a^2=e,c^2=e,d^2=fh,e^2=g,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,d^b=df,f^b=fh,i^c=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81321);