Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1377 ⋊ C2 |
| Sylow | C53 ⋊ #13127 |
300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 95 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)(54,57,58,59,60,67,74,76)(55,62,63,82,64,72,83,65)(56,68,69,85,71,75,70,73)(61,77,66,84,78,79,80,81);(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)(54,56,67,85,74,69,59,75,60,71,57,73,58,70,76,68)(55,61,62,81,83,66,65,77,64,78,72,84,63,80,82,79);(54,55,59,65,58,63,67,62,60,64,76,82,74,83,57,72)(56,66,68,81,70,61,73,79,71,80,75,84,69,78,85,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,c^b=cg,d^b=dh,f^b=fh,i^b=i^52,f^c=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87342);