Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D393 |
| unambiguous semidirect product | C3⋊(C5×D393) |
| Fitting, socle, Hall | C32×C5×C131 ⋊ C2 |
| derived, Hall | C32×C131 ⋊ C2×C5 |
| Hall | C5×C131 ⋊ C3⋊D3 |
| Sylow | C131 ⋊ C5×C3⋊D3 |
| Hall | C32×C5 ⋊ D131 |
| Sylow | C32 ⋊ C5×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D393 |
| commutator, cosocle, hypocenter | C32×C131 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C131 | C2 |
| LCS | G ▷ C32×C131 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
2955 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D393, D15⋊D393, C5×C3⋊D3×D131, … |
| maximal normal subgroup of | C5×D3×D393, D15⋊D393, C5×C3⋊D3×D131, … |
| maximal quotient of | C5×C3⋊Dic393, C2×C5×C3⋊D393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 22);