Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1795 ⋊ C2 |
| Sylow | C53 ⋊ #13099 |
666 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 99 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)(54,57,60,58)(55,62,65,80)(56,67,69,72)(59,73,75,70)(61,76,78,85)(63,64,71,79)(66,81,82,77)(68,84,74,83);(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)(54,56,58,72,60,69,57,67)(55,61,63,66,65,78,71,82)(59,74,73,83,75,68,70,84)(62,76,64,81,80,85,79,77);(54,55)(56,66,69,82)(57,63,58,71)(59,64)(60,65)(61,67)(62,70,80,73)(68,76,74,85)(72,78)(75,79)(77,83)(81,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,f^d=fh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87146);