Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #8101 |
2414 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,b^a=bd,c^a=cg,d^a=dg,f^a=fh,i^a=i^27,d^b=dh,e^b=eg,i^e=i^72772 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1086791);