Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C11⋊(#5997⋊C3) |
| unambiguous semidirect product | C11⋊(C3×#5997⋊C3) |
| unambiguous semidirect product | (C11⋊#5997)⋊C32 |
| unambiguous semidirect product | (C3×C11⋊#5997)⋊C3 |
| Fitting, socle | C3×C72×C11 ⋊ C3×C4 |
| derived, Hall | C72×C11 ⋊ C32×C4 |
| Hall | C3×C11×#3861 ⋊ C4 |
| Hall | C11⋊#5997 ⋊ C32 |
| Hall | C3×#3861 ⋊ Dic11 |
| Sylow | C72 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C3×#5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊(#5997⋊C3) |
| commutator, hypocenter | C72×C11 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C3×C4 |
| prime radical | C3×C11×#64424 | C2 |
| cosocle | C11×C7⋊D7 | C2×C32 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 462 |
258 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 349);