Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1378 ⋊ C2 |
| Sylow | C53 ⋊ #13129 |
306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 306 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)(54,57,58,65)(55,61)(56,67)(59,74,66,71)(60,72,73,81)(62,68)(63,69)(64,77)(70,80)(75,85,82,83)(76,78)(79,84);(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)(54,56,66,68,60,69,82,84,58,70,59,61,73,76,75,77)(55,57,63,74,64,72,80,85,62,65,78,71,79,81,67,83);(54,55,59,63,60,64,75,80,58,62,66,78,73,79,82,67)(56,65,68,74,69,81,84,85,70,57,61,71,76,72,77,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cg,d^b=dh,f^b=fh,i^b=i^52,e^c=eh,f^c=fh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87356);