Finite Group DatabasebetaFinite Group Databasebeta| order | 34542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5757 |
| unambiguous semidirect product | C19⋊(C3⋊D303) |
| unambiguous semidirect product | C101⋊(C3⋊D57) |
| Fitting, socle, derived, Hall | C32×C19×C101 ⋊ C2 |
| Hall | C19×C101 ⋊ C3⋊D3 |
| Hall | C32×C101 ⋊ D19 |
| Hall | C32×C19 ⋊ D101 |
| Sylow | C101 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊D303 |
| Sylow | C32 ⋊ D1919 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C19×C101 | C2 |
| LCS | G ▷ C32×C19×C101 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17271 |
Polycyclic presentation:
2,3^2,19,101|b^a=b^2,c^a=c^2,d^a=d^18,e^a=e^1008637 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34542, 36);