Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#3162 ⋊ C2 |
| Sylow | C53 ⋊ #13373 |
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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)(55,61)(57,72)(58,69)(59,66)(60,67)(62,79)(63,80)(64,77)(65,81)(68,73)(70,82)(71,85)(74,84)(75,76)(78,83);(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)(56,66,67,69)(57,71)(61,76,77,80)(62,78)(65,79,82,83)(68,85,84,72)(70,81)(73,74);(54,55)(56,65,67,82)(57,70)(58,63)(59,75)(60,64)(61,68,77,84)(62,74)(66,83,69,79)(71,81)(72,80,85,76)(73,78)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=cf,e^b=eh,d^c=dh,e^c=egh,f^c=fh,g^c=gh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88683);