Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C19 |
| direct product | C5×C3⋊(C19⋊D19) |
| unambiguous semidirect product | C3⋊(C5×C19⋊D19) |
| unambiguous semidirect product | C19⋊(C5×D57) |
| Fitting, socle, Hall | C3×C5×C192 ⋊ C2 |
| derived, Hall | C3×C192 ⋊ C2×C5 |
| Hall | C5×C192 ⋊ D3 |
| Sylow | C192 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ C19⋊D19 |
| Sylow | C3 ⋊ C5×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C19⋊D19) |
| commutator, cosocle, hypocenter | C3×C192 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C192 | C2 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C5 | |
176 conjugacy classes of subgroups.
2715 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D57, C5×D3×C19⋊D19, D95⋊D57, … |
| maximal normal subgroup of | C5×D19×D57, C5×D3×C19⋊D19, D95⋊D57, … |
| maximal quotient of | C5×C3⋊(C19⋊Dic19), C2×C5×C3⋊(C19⋊D19), C5×C9⋊(C19⋊D19), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 48);