Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D5×C31×D19 |
| unambiguous semidirect product | (D5×C19)⋊(C2×C31) |
| unambiguous semidirect product | (C5×D19)⋊(C2×C31) |
| unambiguous semidirect product | D95⋊(C2×C31) |
| Fitting, socle, Hall | C5×C19×C31 ⋊ C22 |
| derived, Hall | C5×C19 ⋊ C22×C31 |
| Hall | C19×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D5×C31 |
| Sylow | C5 ⋊ C2×C31×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D5×D19 |
| commutator, cosocle, hypocenter | C5×C19 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C31 | C22 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C31 | |
40 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C31×D19⋊C3, D5×#16812972, D5×#16812971, … |
| maximal normal subgroup of | D5×C31×D19⋊C3, D5×#16812972, D5×#16812971, … |
| maximal quotient of | C3×D5×C31×D19, D15×C31×D19, D5×C31×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 26);