Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C16×C73 ⋊ C8 |
| Sylow | C73 ⋊ #11405 |
282 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 282 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.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,e^a=eh,c^b=ch,d^b=dh,i^b=i^10,i^e=i^27,i^g=i^72376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117080);