Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic11×#89204 |
| unambiguous semidirect product | C11⋊(C4×#89204) |
| derived, Hall | C72×C11 ⋊ C4×C9 |
| Hall | C11×#89204 ⋊ C4 |
| Hall | C72×Dic11 ⋊ C9 |
| Sylow | C72 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ C4×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D11×#3861 |
| commutator, hypocenter | C72×C11 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C72×C11 | C2×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2×C3 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19404 |
798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 126);