Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13175 |
256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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:
(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)(54,56,58,65,59,69,72,82,60,68,74,81,57,67,71,80)(55,62,63,77,61,66,75,76,64,78,73,85,70,83,84,79);(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)(54,55)(56,66,68,83)(57,70)(58,73)(59,61)(60,64)(62,69,78,67)(63,74)(65,79,81,76)(71,75)(72,84)(77,80,85,82);(55,61)(56,65,68,81)(57,59)(58,72)(62,76,78,79)(63,73)(64,70)(66,77,83,85)(67,82,69,80)(71,74)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,c^b=cg,d^b=dh,e^b=eh,f^c=fh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87647);