Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13154 |
314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 314 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) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(55,57)(58,61,62,74,63,78,81,75,64,79,72,73,82,77,89,60)(59,66,67,76,69,84,80,88,70,85,87,65,68,71,86,83);(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)(58,60,72,61,63,74,89,78,64,75,62,79,82,73,81,77)(59,65,67,84,69,83,80,85,70,76,87,71,68,88,86,66);(54,55)(56,57)(58,59,63,68,64,70,82,69)(60,71,73,66,75,84,74,85)(61,76,77,88,79,65,78,83)(62,80,81,67,72,86,89,87)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=d,d^2=g,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,f^c=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87531);