Finite Group DatabasebetaFinite Group Databasebeta| order | 30849 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×C113⋊C7 |
| unambiguous semidirect product | C113⋊(C3×C7×C13) |
| unambiguous semidirect product | (C3×C113)⋊(C7×C13) |
| unambiguous semidirect product | (C3×C13×C113)⋊C7 |
| Fitting, socle, Hall | C3×C13×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C3×C7×C13 |
| Hall | C13×C113 ⋊ C3×C7 |
| Hall | C3×C113 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C113⋊C7 |
| commutator, cosocle, hypocenter | C113 | C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C3×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4407 |
897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30849, 2);