Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #13646 |
202 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 91 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:
(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)(58,60,62,71,63,72,76,86,64,65,69,78,77,79,84,88,61,70,73,80,74,85,87,89,75,59,66,67,81,68,82,83);(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)(55,57)(59,65)(60,70)(67,78)(68,79)(71,80)(72,85)(83,88)(86,89);(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)(58,59,62,67,63,68,76,83,64,60,69,71,77,72,84,86,61,65,73,78,74,79,87,88,75,70,66,80,81,85,82,89)Polycyclic presentation:
2^8,53|a^2=e,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^52,c^b=ch,i^b=i^523440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90128);