Finite Group DatabasebetaFinite Group Databasebeta| order | 30396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C149 · Schur multiplier (H2) = C1 |
| direct product | C149×Dic51 |
| unambiguous semidirect product | C3⋊(Dic17×C149) |
| derived, Hall | C3×C17 ⋊ C4×C149 |
| Hall | C3×C17×C149 ⋊ C4 |
| Hall | C17×C149 ⋊ Dic3 |
| Hall | C3×C149 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C149 |
| Sylow | C3 ⋊ Dic17×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C149 | D51 |
| commutator, hypocenter | C3×C17 | C4×C149 |
| Frattini | C2 | D51×C149 |
| Fitting, socle, prime radical | C2×C3×C17×C149 | C2 |
| cosocle | C2×C3×C17 | C2×C149 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C149 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30396 |
8046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30396, 7);