Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C42×C73 ⋊ C4 |
| Sylow | C73 ⋊ #10726 |
1510 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1510 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^27,f^b=fh,i^f=i^721216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1091941);