Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×C22⋊(C361⋊C3) |
| unambiguous semidirect product | C22⋊(C7×C361⋊C3) |
| unambiguous semidirect product | C361⋊(C7×A4) |
| Fitting, Hall | C22×C7×C361 ⋊ C3 |
| derived, Hall | C22×C361 ⋊ C3×C7 |
| Hall | C7×C361 ⋊ A4 |
| Sylow | C361 ⋊ C7×A4 |
| Hall | C22×C7 ⋊ C361⋊C3 |
| Sylow | C22 ⋊ C7×C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C22⋊(C361⋊C3) |
| commutator, cosocle, hypocenter | C22×C361 | C3×C7 |
| Frattini | C19 | C7×C22⋊(C19⋊C3) |
| Fitting | C22×C7×C361 | C3 |
| socle | C22×C7×C19 | C19⋊C3 |
| LCS | G ▷ C22×C361 | |
| UCS | C1 ◁ C7 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10108 |
3388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 54);