Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C13 |
| direct product | C3×C5×#14523161 |
| Fitting, socle | C3×C5×C132 ⋊ Dic3 |
| derived | #92789 ⋊ C3×C4×C5 |
| Hall | C3×C5×#92789 ⋊ C4 |
| Hall | C3×#92789 ⋊ C4×C5 |
| Hall | C5×C132 ⋊ C3×Dic3 |
| Sylow | C132 ⋊ C3×C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #14523161 |
| commutator, hypocenter | #92789 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | Dic3 |
| prime radical | C3×C5×#11759816 | C2 |
| cosocle | #11759816 | C2×C3×C5 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C3×C5 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 390 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 495);