Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16813380 |
| Fitting, socle, Hall | C3×C192 ⋊ D5 |
| derived, Hall | C3×C192⋊C5 ⋊ C2 |
| Hall | C192⋊C5 ⋊ D3 |
| Sylow | C192 ⋊ D15 |
| Sylow | C3 ⋊ #16813380 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C192⋊C5 | C2 |
| Fitting, socle | C3×C192 | D5 |
| LCS | G ▷ C3×C192⋊C5 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|b^a=b^2,c^a=c^4,d^a=d^8e^3,e^a=d^17e^11,d^c=d^16e^4,e^c=d^4e^7144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 19);