Finite Group DatabasebetaFinite Group Databasebeta| order | 11490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1915 |
| unambiguous semidirect product | C5⋊(C3×D383) |
| unambiguous semidirect product | C383⋊(C3×D5) |
| Fitting, socle, Hall | C3×C5×C383 ⋊ C2 |
| derived, Hall | C5×C383 ⋊ C2×C3 |
| Hall | C3×C383 ⋊ D5 |
| Sylow | C383 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ D383 |
| Sylow | C5 ⋊ C3×D383 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1915 |
| commutator, cosocle, hypocenter | C5×C383 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C383 | C2 |
| LCS | G ▷ C5×C383 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2877 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D383, D3×D1915, D15⋊D383, … |
| maximal normal subgroup of | C3×D5×D383, D3×D1915, D15⋊D383, … |
| maximal quotient of | C3×Dic1915, C2×C3×D1915, C9×D1915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11490, 4);