Finite Group DatabasebetaFinite Group Databasebeta| order | 30150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C67 · Schur multiplier (H2) = C5 |
| direct product | D3×C67×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C67×C52⋊C3) |
| unambiguous semidirect product | (C52×D3)⋊(C3×C67) |
| Fitting, socle | C3×C52×C67 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C67 |
| Hall | C3×C67×C52⋊C3 ⋊ C2 |
| Hall | C52×C67 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C67 |
| Sylow | C52 ⋊ C3×D3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D3×C52⋊C3 |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C67 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C67 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C67 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3015 |
2211 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30150, 81);