Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #12633 |
460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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=e,b^2=f,c^2=e,d^2=h,e^2=h,b^a=bd,d^a=dh,f^a=fgh,i^a=i^72,d^b=dg,g^b=gh,i^b=i^27,f^d=fh,i^f=i^721204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1096128);