Finite Group DatabasebetaFinite Group Databasebeta| order | 19065 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×C31⋊C3) |
| unambiguous semidirect product | (C31×C41⋊C5)⋊C3 |
| Fitting, socle, derived, Hall | C31×C41 ⋊ C3×C5 |
| Hall | C31×C41⋊C5 ⋊ C3 |
| Hall | C41×C31⋊C3 ⋊ C5 |
| Sylow | C41 ⋊ C5×C31⋊C3 |
| Sylow | C31 ⋊ C3×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C41 | C3×C5 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1271 |
169 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31⋊C3×C41⋊C5, C31⋊C3×D41⋊C5, D31⋊C3×C41⋊C5, … |
| maximal normal subgroup of | C2×C31⋊C3×C41⋊C5, C31⋊C3×D41⋊C5, D31⋊C3×C41⋊C5, … |
| maximal quotient of | C2×C31⋊C3×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19065, 9);