Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1388 ⋊ C2 |
| Sylow | C53 ⋊ #13158 |
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,57,58,72,60,75,77,73,61,76,67,80,79,74,59,78)(55,62,56,68,65,81,69,71,66,82,70,85,64,84,63,83);(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)(54,56,58,64,60,69,77,55,61,70,67,65,79,63,59,66)(57,71,80,82,75,85,78,84,76,83,72,62,74,68,73,81);(54,55,60,64,61,66,79,65)(56,67,63,59,70,58,69,77)(57,71,74,85,76,83,75,68)(62,80,81,73,82,72,84,78)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,c^2=d,d^2=g,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,e^c=eh,f^c=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87559);