Finite Group DatabasebetaFinite Group Databasebeta| order | 16390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D745 |
| unambiguous semidirect product | C5⋊(C11×D149) |
| unambiguous semidirect product | C149⋊(D5×C11) |
| Fitting, socle, Hall | C5×C11×C149 ⋊ C2 |
| derived, Hall | C5×C149 ⋊ C2×C11 |
| Hall | C11×C149 ⋊ D5 |
| Sylow | C149 ⋊ D5×C11 |
| Hall | C5×C11 ⋊ D149 |
| Sylow | C5 ⋊ C11×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D745 |
| commutator, cosocle, hypocenter | C5×C149 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C149 | C2 |
| LCS | G ▷ C5×C149 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8195 |
4114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15688381, C11×#15688382, C11⋊#15688381, … |
| maximal normal subgroup of | C11×#15688381, C11×#15688382, C11⋊#15688381, … |
| maximal quotient of | C11×Dic745, C2×C11×D745 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16390, 7);