Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊((C19⋊D19)⋊C5) |
| unambiguous semidirect product | (C3⋊(C19⋊D19))⋊C5 |
| Fitting, socle, derived, Hall | C3×C192 ⋊ C2×C5 |
| Hall | C3×C192⋊C5 ⋊ C2 |
| Hall | C3⋊(C19⋊D19) ⋊ C5 |
| Hall | C192⋊C5 ⋊ D3 |
| Sylow | C192 ⋊ C5×D3 |
| Sylow | C3 ⋊ (C19⋊D19)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C192 | C2×C5 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,19^2|c^a=c^2,d^a=d^18,e^a=e^18,d^b=d^12e^8,e^b=d^14e^11123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 20);