Finite Group DatabasebetaFinite Group Databasebeta| order | 30414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C137) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C137) |
| unambiguous semidirect product | (D37×C137)⋊C3 |
| Fitting, socle, Hall | C37×C137 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C137 |
| Hall | C37⋊C3×C137 ⋊ C2 |
| Hall | D37×C137 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C137 |
| Hall | D37 ⋊ C3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C37×C137 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C137 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5069 |
1644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30414, 11);