Finite Group DatabasebetaFinite Group Databasebeta| order | 30414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×D137 |
| unambiguous semidirect product | C137⋊(C2×C37⋊C3) |
| unambiguous semidirect product | (C37×D137)⋊C3 |
| Fitting, socle, derived, Hall | C37×C137 ⋊ C2×C3 |
| Hall | C37⋊C3×C137 ⋊ C2 |
| Hall | C37×D137 ⋊ C3 |
| Sylow | C137 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ C3×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C137 | C2×C3 |
| LCS | G ▷ C37×C137 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5069 |
1050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30414, 10);