Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D57⋊D19 |
| unambiguous semidirect product | D57⋊(C7×D19) |
| Fitting, socle, Hall | C3×C7×C192 ⋊ C22 |
| derived, Hall | C3×C192 ⋊ C22×C7 |
| Hall | C7×C192 ⋊ C2×D3 |
| Sylow | C192 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ D192 |
| Sylow | C3 ⋊ C7×D192 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D57⋊D19 |
| commutator, cosocle, hypocenter | C3×C192 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C192 | C22 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C7 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
2121 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 274);