Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C31×Dic19 |
| unambiguous semidirect product | C19⋊(C4×C5×C31) |
| derived, Sylow | C19 ⋊ C4×C5×C31 |
| Hall | C5×C19×C31 ⋊ C4 |
| Hall | C19×C31 ⋊ C4×C5 |
| Hall | C5×C19 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C31 | D19 |
| commutator, hypocenter | C19 | C4×C5×C31 |
| Frattini | C2 | C5×C31×D19 |
| Fitting, socle, prime radical | C2×C5×C19×C31 | C2 |
| cosocle | C2×C19 | C2×C5×C31 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C5×C31 | |
24 conjugacy classes of subgroups.
3410 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C31×Dic19, C5×C31×Dic57, C5×Dic19×C31⋊C3, … |
| maximal normal subgroup of | C3×C5×C31×Dic19, C5×Dic19×C31⋊C3, C5×C31×(C19⋊C3)⋊C4, … |
| maximal quotient of | C3×C5×C31×Dic19, C5×C31×Dic57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 4);