Finite Group DatabasebetaFinite Group Databasebeta| order | 30678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C5113⋊C3 |
| unambiguous semidirect product | (C2×C5113)⋊C3 |
| Fitting, socle, Hall | C2×C5113 ⋊ C3 |
| derived, Sylow | C5113 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5113⋊C3 |
| commutator, cosocle, hypocenter | C5113 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5113 | C3 |
| LCS | G ▷ C5113 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10226 |
3414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30678, 2);