Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2133 ⋊ C2 |
| Sylow | C53 ⋊ #12710 |
952 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 107 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)(54,57,60,59)(55,62,65,64)(56,67,69,75)(58,73,74,70)(61,77,78,79)(63,82,71,80)(66,83,81,84)(68,76,72,85);(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)(54,56)(55,61)(57,67)(58,72)(59,75)(60,69)(62,77)(63,81)(64,79)(65,78)(66,71)(68,74)(70,76)(73,85)(80,83)(82,84);(54,55,59,64,60,65,57,62)(56,66,67,84,69,81,75,83)(58,71,70,82,74,63,73,80)(61,76,79,72,78,85,77,68)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,i^c=i^52,f^d=fh632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85109);