Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#323×C73 ⋊ C2 |
| Sylow | C73 ⋊ #18285 |
1408 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 187 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=g,e^2=g,b^a=be,c^a=cf,d^a=dh,e^a=eg,i^a=i^72,e^b=eg,f^b=fh,i^b=i^72,e^c=eh1624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 143412);