Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D361⋊C3) |
| unambiguous semidirect product | (C361⋊C3)⋊D5 |
| unambiguous semidirect product | D1805⋊C3 |
| Fitting, derived, Hall | C5×C361 ⋊ C2×C3 |
| Hall | C5×C361⋊C3 ⋊ C2 |
| Hall | D1805 ⋊ C3 |
| Hall | C361⋊C3 ⋊ D5 |
| Sylow | C361 ⋊ C3×D5 |
| Sylow | C5 ⋊ D361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C361 | C2×C3 |
| Frattini | C19 | C5⋊(D19⋊C3) |
| socle | C5×C19 | D19⋊C3 |
| LCS | G ▷ C5×C361 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|d^19=e^18,c^a=c^4,d^a=d^18e,e^a=e^18,d^b=d^7e^4,e^b=e^7312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 4);