Finite Group DatabasebetaFinite Group Databasebeta| order | 33570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5595 |
| unambiguous semidirect product | C5⋊(C3⋊D1119) |
| unambiguous semidirect product | C373⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C5×C373 ⋊ C2 |
| Hall | C32×C373 ⋊ D5 |
| Hall | C5×C373 ⋊ C3⋊D3 |
| Sylow | C373 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D373 |
| Sylow | C32 ⋊ D1865 |
| Sylow | C5 ⋊ C3⋊D1119 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C373 | C2 |
| LCS | G ▷ C32×C5×C373 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16785 |
Polycyclic presentation:
2,3^2,5,373|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^3728394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33570, 32);