Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12596 |
310 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 147 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61,62,63,64,78,79,80)(59,66,67,85,69,68,70,76)(60,72,73,87,75,77,88,74)(65,81,71,86,82,84,83,89);(54,55,56,57)(58,60)(59,65,69,82)(61,77)(62,73)(63,74)(64,75)(66,84,68,81)(67,71,70,83)(72,78)(76,86,85,89)(79,88)(80,87);(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)(58,59,63,68,62,70,78,85,64,69,80,66,79,67,61,76)(60,71,74,86,73,65,72,81,75,83,87,89,88,82,77,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=d,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=dh,f^a=fh,i^a=i^52,c^b=ch,e^c=eh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84588);