Finite Group DatabasebetaFinite Group Databasebeta| order | 30966 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D397⋊C3 |
| unambiguous semidirect product | D397⋊(C3×C13) |
| unambiguous semidirect product | (C397⋊C3)⋊(C2×C13) |
| Fitting, socle, Hall | C13×C397 ⋊ C2×C3 |
| derived, Sylow | C397 ⋊ C2×C3×C13 |
| Hall | C13×C397⋊C3 ⋊ C2 |
| Hall | C13×D397 ⋊ C3 |
| Hall | C397⋊C3 ⋊ C2×C13 |
| Hall | D397 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D397⋊C3 |
| commutator, cosocle, hypocenter | C397 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C397 | C2×C3 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5161 |
936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30966, 13);