Finite Group DatabasebetaFinite Group Databasebeta| order | 3690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D123 |
| unambiguous semidirect product | C3⋊(C5×D123) |
| Fitting, socle, Hall | C32×C5×C41 ⋊ C2 |
| derived, Hall | C32×C41 ⋊ C2×C5 |
| Hall | C5×C41 ⋊ C3⋊D3 |
| Hall | C32×C5 ⋊ D41 |
| Sylow | C41 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ C5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D123 |
| commutator, cosocle, hypocenter | C32×C41 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C2 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3690, 28);