Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D95 |
| unambiguous semidirect product | C5⋊(D19×C19⋊C3) |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C3 |
| Hall | C5×C19×C19⋊C3 ⋊ C2 |
| Hall | C19×D95 ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ D5 |
| Sylow | C192 ⋊ C3×D5 |
| Sylow | C5 ⋊ D19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C192 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
441 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D95, (C5⋊(D19⋊C3))⋊D19, D5×D19×C19⋊C3, … |
| maximal normal subgroup of | D19⋊C3×D95, (C5⋊(D19⋊C3))⋊D19, D5×D19×C19⋊C3, … |
| maximal quotient of | C19⋊C3×Dic95, C2×C19⋊C3×D95, #4294×D95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 39);