Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C73×#2405 ⋊ C2 |
| Sylow | C73 ⋊ #10337 |
1274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1274 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,e^b=eh,d^c=dg,i^c=i^721402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 72522);