Finite Group DatabasebetaFinite Group Databasebeta| order | 19596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊D71 |
| unambiguous semidirect product | D213⋊D23 |
| unambiguous semidirect product | D1633⋊D3 |
| Fitting, socle, derived, Hall | C3×C23×C71 ⋊ C22 |
| Hall | C23×C71 ⋊ C2×D3 |
| Hall | C3×C71 ⋊ C2×D23 |
| Sylow | C71 ⋊ D3×D23 |
| Hall | C3×C23 ⋊ C2×D71 |
| Sylow | C23 ⋊ D3×D71 |
| Sylow | C3 ⋊ D23×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C71 | C22 |
| LCS | G ▷ C3×C23×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4899 |
Polycyclic presentation:
2^2,3,23,71|d^a=d^22,e^a=e^70,c^b=c^2,d^b=d^221299 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19596, 16);