Finite Group DatabasebetaFinite Group Databasebeta| order | 30378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×C83) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C83) |
| unambiguous semidirect product | (C83×D61)⋊C3 |
| Fitting, socle, Hall | C61×C83 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C3×C83 |
| Hall | C83×C61⋊C3 ⋊ C2 |
| Hall | C83×D61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C2×C83 |
| Hall | D61 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C61×C83 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C83 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5063 |
1328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30378, 11);