Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×M32×C73 ⋊ C4 |
| Sylow | C73 ⋊ #7228 |
252 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 58 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=d,b^2=e,c^2=fgh,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efgh,g^a=gh,i^a=i^27,d^b=dg,i^b=i^72,d^c=dh,i^d=i^72760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1084041);