Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D155 |
| unambiguous semidirect product | (C5×D19)⋊D31 |
| unambiguous semidirect product | (C31×D19)⋊D5 |
| Fitting, socle, derived, Hall | C5×C19×C31 ⋊ C22 |
| Hall | C19×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D19 |
| Sylow | C19 ⋊ C2×D155 |
| Sylow | C5 ⋊ D19×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C31 | C22 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
869 conjugacy classes — view the full character table.
| maximal subgroup of | #16812972⋊D5, #16812971⋊D5, D19⋊C3×D155, … |
| maximal normal subgroup of | #16812972⋊D5, #16812971⋊D5, D19⋊C3×D155, … |
| maximal quotient of | C3×D19×D155, D19×D465, D57×D155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 27);