Finite Group DatabasebetaFinite Group Databasebeta| order | 30150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3⋊(C5⋊D5)×C67⋊C3 |
| unambiguous semidirect product | C3⋊(C5⋊D5×C67⋊C3) |
| unambiguous semidirect product | C5⋊(D15×C67⋊C3) |
| Fitting, socle, derived | C3×C52×C67 ⋊ C2×C3 |
| Hall | C3×C52×C67⋊C3 ⋊ C2 |
| Hall | C52×C67 ⋊ C3×D3 |
| Hall | C3×C67⋊C3 ⋊ C5⋊D5 |
| Sylow | C67 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ D3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C67 | C2×C3 |
| LCS | G ▷ C3×C52×C67 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5025 |
975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30150, 96);