Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3407 ⋊ C2 |
| Sylow | C53 ⋊ #13077 |
470 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 127 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)(55,62)(56,68)(58,77)(59,73)(60,74)(61,79)(63,70)(64,69)(65,81)(66,67)(71,84)(72,78)(75,85)(76,80)(82,83);(54,56,67,62,79,85,58,76,59,70,83,81,60,71,78,69)(55,61,75,77,80,73,63,82,65,74,84,72,64,57,68,66);(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)(56,66,70,82)(57,62,73,81)(58,75)(59,65)(60,80)(61,69,74,76)(63,67)(64,79)(68,83)(71,77,85,72)(78,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^52,d^b=dh,e^b=eh,f^b=fh,d^c=dh,f^c=fh1814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87032);