Finite Group DatabasebetaFinite Group Databasebeta| order | 30180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D503 |
| unambiguous semidirect product | (D5×C503)⋊(C2×C3) |
| unambiguous semidirect product | (C5×D503)⋊(C2×C3) |
| unambiguous semidirect product | D2515⋊(C2×C3) |
| Fitting, socle, Hall | C3×C5×C503 ⋊ C22 |
| derived, Hall | C5×C503 ⋊ C22×C3 |
| Hall | C3×C503 ⋊ C2×D5 |
| Sylow | C503 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ C2×D503 |
| Sylow | C5 ⋊ C2×C3×D503 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D503 |
| commutator, cosocle, hypocenter | C5×C503 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C503 | C22 |
| LCS | G ▷ C5×C503 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7545 |
3036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30180, 12);