Finite Group DatabasebetaFinite Group Databasebeta| order | 30174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C107 · Schur multiplier (H2) = C1 |
| direct product | C3×D47×C107 |
| unambiguous semidirect product | C47⋊(C2×C3×C107) |
| Fitting, socle, Hall | C3×C47×C107 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C3×C107 |
| Hall | C47×C107 ⋊ C2×C3 |
| Hall | C3×C47 ⋊ C2×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C107 | D47 |
| commutator, cosocle, hypocenter | C47 | C2×C3×C107 |
| Frattini | C1 | G |
| Fitting, socle | C3×C47×C107 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C3×C107 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15087 |
8025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30174, 3);