Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2110 ⋊ C2 |
| Sylow | C53 ⋊ #13200 |
438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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)(54,57,58,72,61,71,60,74)(55,63,64,69,56,66,67,70)(59,73,75,78,62,77,76,81)(65,79,80,84,68,82,83,85);(54,56,59,68,60,67,76,83,61,55,62,65,58,64,75,80)(57,70,77,84,74,63,78,82,71,69,73,85,72,66,81,79);(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)(54,55,59,65,60,64,76,80,61,56,62,68,58,67,75,83)(57,69,73,84,74,66,81,82,71,70,77,85,72,63,78,79)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=e,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87773);