Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C151 ⋊ #2100 |
214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 19328 |
Polycyclic presentation:
2^7,151|a^2=d,b^2=deg,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^150,f^c=fg,h^c=h^1503032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 6074);