Finite Group DatabasebetaFinite Group Databasebeta| order | 3330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊(D37⋊C3)) |
| unambiguous semidirect product | C5⋊(C3⋊(D37⋊C3)) |
| unambiguous semidirect product | (C37⋊C3)⋊D15 |
| unambiguous semidirect product | D555⋊C3 |
| Fitting, socle, derived | C3×C5×C37 ⋊ C2×C3 |
| Hall | C3×C5×C37⋊C3 ⋊ C2 |
| Hall | C3×C37⋊C3 ⋊ D5 |
| Hall | C5×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3⋊(D37⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C37 | C2×C3 |
| LCS | G ▷ C3×C5×C37 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 555 |
Polycyclic presentation:
2,3^2,5,37|c^a=c^2,d^a=d^4,e^a=e^36,e^b=e^26117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3330, 23);