Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #382×C73 ⋊ C4 |
| Sylow | C73 ⋊ #10893 |
762 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 170 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=f,b^2=g,c^2=f,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^72,d^b=dh,e^b=eh,i^b=i^27,d^c=dh,i^g=i^72568 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1092454);