Finite Group DatabasebetaFinite Group Databasebeta| order | 30134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C19 · Schur multiplier (H2) = C1 |
| direct product | C13×C19×D61 |
| unambiguous semidirect product | C61⋊(C2×C13×C19) |
| Fitting, socle, Hall | C13×C19×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C13×C19 |
| Hall | C19×C61 ⋊ C2×C13 |
| Hall | C13×C61 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C19 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C13×C19 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C13×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15067 |
7904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30134, 2);