Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #353×C151 ⋊ C2 |
| Sylow | C151 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1208 |
Polycyclic presentation:
2^7,151|b^a=bd,c^a=ce,f^a=fg,h^a=h^150,e^b=efg,h^b=h^150,d^c=df,h^c=h^150,e^d=eg995 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 6496);