Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1785 ⋊ C2 |
| Sylow | C53 ⋊ #12709 |
986 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 111 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)(57,70)(61,68)(64,78)(65,69)(71,73)(75,83)(79,80)(82,84);(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)(55,60)(57,69)(58,72)(59,66)(61,78)(62,77)(63,76)(64,68)(65,70)(67,74)(71,75)(73,83)(79,84)(80,82)(81,85);(54,55,58,62,59,63,74,81)(56,64,67,82,66,78,72,84)(57,68,71,80,70,61,73,79)(60,75,77,69,76,83,85,65)Polycyclic presentation:
2^8,53|a^2=f,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,i^b=i^52,d^c=dh,f^d=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85107);