Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D133⋊D57 |
| Fitting, socle, derived, Hall | C3×C7×C192 ⋊ C22 |
| Hall | C7×C192 ⋊ C2×D3 |
| Hall | C3×C192 ⋊ C2×D7 |
| Sylow | C192 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ D192 |
| Sylow | C7 ⋊ D19×D57 |
| Sylow | C3 ⋊ D133⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C192 | C22 |
| LCS | G ▷ C3×C7×C192 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2^2,3,7,19^2|d^a=d^6,e^a=e^18,c^b=c^2,e^b=e^18,f^b=f^181959 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 286);