Finite Group DatabasebetaFinite Group Databasebeta| order | 30150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | C2×C52⋊(C67⋊C9) |
| unambiguous semidirect product | (C2×C52)⋊(C67⋊C9) |
| unambiguous semidirect product | (C2×C67)⋊(C52⋊C9) |
| derived, Hall | C52×C67 ⋊ C2×C9 |
| Hall | C2×C52×C67 ⋊ C9 |
| Hall | C2×C67 ⋊ C52⋊C9 |
| Sylow | C67 ⋊ C2×C52⋊C9 |
| Hall | C2×C52 ⋊ C67⋊C9 |
| Sylow | C52 ⋊ C2×C67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C52⋊(C67⋊C3) |
| commutator, hypocenter | C52×C67 | C2×C9 |
| Frattini | C3 | C2×C52⋊(C67⋊C3) |
| Fitting, socle, prime radical | C2×C3×C52×C67 | C3 |
| cosocle | C3×C52×C67 | C2×C3 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6030 |
3366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30150, 47);