Finite Group DatabasebetaFinite Group Databasebeta| order | 18612 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1551 |
| unambiguous semidirect product | C3⋊(C3×Dic517) |
| unambiguous semidirect product | C11⋊(C3×Dic141) |
| unambiguous semidirect product | C47⋊(C3×Dic33) |
| derived | C3×C11×C47 ⋊ C3×C4 |
| Hall | C32×C11×C47 ⋊ C4 |
| Hall | C11×C47 ⋊ C3×Dic3 |
| Hall | C32×C47 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic47 |
| Sylow | C47 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ C3×Dic141 |
| Sylow | C32 ⋊ Dic517 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1551 |
| commutator, hypocenter | C3×C11×C47 | C3×C4 |
| Frattini | C2 | C3×D1551 |
| Fitting, socle, prime radical | C2×C32×C11×C47 | C2 |
| cosocle | C2×C3×C11×C47 | C2×C3 |
| LCS | G ▷ C3×C11×C47 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6204 |
4662 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18612, 32);