Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D361 |
| unambiguous semidirect product | D1083⋊D7 |
| unambiguous semidirect product | D2527⋊D3 |
| Fitting, derived, Hall | C3×C7×C361 ⋊ C22 |
| Hall | C7×C361 ⋊ C2×D3 |
| Hall | C3×C361 ⋊ C2×D7 |
| Sylow | C361 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D361 |
| Sylow | C7 ⋊ D3×D361 |
| Sylow | C3 ⋊ D7×D361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C361 | C22 |
| Frattini | C19 | D21⋊D19 |
| socle | C3×C7×C19 | C2×D19 |
| LCS | G ▷ C3×C7×C361 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7581 |
Polycyclic presentation:
2^2,3,7,19^2|e^19=f^18,d^a=d^6,e^a=e^18f,f^a=f^18,c^b=c^2,d^b=d^62175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 48);