Finite Group DatabasebetaFinite Group Databasebeta| order | 30734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×D121 |
| unambiguous semidirect product | C121⋊(C2×C127) |
| Fitting, Hall | C121×C127 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C127 |
| Frattini | C11 | D11×C127 |
| Fitting | C121×C127 | C2 |
| socle | C11×C127 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C127 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15367 |
7874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30734, 2);