Finite Group DatabasebetaFinite Group Databasebeta| order | 30540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C509 · Schur multiplier (H2) = C1 |
| direct product | Dic15×C509 |
| unambiguous semidirect product | C3⋊(Dic5×C509) |
| derived, Hall | C3×C5 ⋊ C4×C509 |
| Hall | C3×C5×C509 ⋊ C4 |
| Hall | C5×C509 ⋊ Dic3 |
| Hall | C3×C509 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C509 |
| Sylow | C3 ⋊ Dic5×C509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C509 | D15 |
| commutator, hypocenter | C3×C5 | C4×C509 |
| Frattini | C2 | D15×C509 |
| Fitting, socle, prime radical | C2×C3×C5×C509 | C2 |
| cosocle | C2×C3×C5 | C2×C509 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C509 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30540 |
9162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30540, 7);