Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#368 ⋊ C2 |
| Sylow | C53 ⋊ #12842 |
366 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61)(59,64)(60,71)(62,76)(63,67)(65,74)(66,78)(68,75)(69,83)(70,82)(72,86)(73,80)(77,87)(79,84)(81,89)(85,88);(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)(58,60,70,79,63,73,78,83,64,74,87,88,75,89,62,72)(59,65,77,85,68,81,76,86,61,71,82,84,67,80,66,69);(54,55,56,57)(58,59,63,67,64,61,75,68)(60,69,73,84,74,86,89,85)(62,77,70,66,78,82,87,76)(65,79,80,83,71,88,81,72)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,e^c=eh,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85767);