Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3407 ⋊ C2 |
| Sylow | C53 ⋊ #12988 |
466 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 135 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,56)(58,76)(59,66)(60,72)(61,74)(62,67)(63,71)(64,69)(65,83)(68,75)(70,82)(73,78)(77,81)(79,80)(84,85);(54,56,67,79,58,68,78,83,61,69,77,85,60,71,59,70)(55,62,80,76,75,73,65,74,64,81,84,72,63,66,82,57);(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)(54,55,59,65,60,63,77,80,61,64,78,82,58,75,67,84)(56,66,70,76,71,81,85,57,69,73,83,72,68,62,79,74)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^52,e^b=eh,d^c=dh,f^c=fh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86491);