Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12657 |
334 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 334 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)(58,61,62,63,64,76,77,79)(59,66,67,78,69,83,84,68)(60,71,86,87,73,74,72,75)(65,80,85,88,81,89,70,82);(55,57)(58,60,63,74,62,72,76,87,64,73,79,71,77,86,61,75)(59,65,68,80,67,70,66,82,69,81,78,89,84,85,83,88);(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)(54,55,56,57)(58,59)(60,70,73,85)(61,66)(62,67)(63,78)(64,69)(65,72,81,86)(68,79)(71,82,74,88)(75,89,87,80)(76,83)(77,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=de,d^2=h,f^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^52,c^b=cg,e^b=eh,f^c=fh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84895);