Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16813380⋊C3 |
| Fitting, socle, Sylow | C192 ⋊ C3×D5 |
| derived, Hall | C192⋊C5 ⋊ C2×C3 |
| Hall | #11762245⋊C5 ⋊ C2 |
| Hall | #16813380 ⋊ C3 |
| Hall | #11762245 ⋊ D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C192⋊C5 | C2×C3 |
| Fitting, socle | C192 | C3×D5 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|c^a=c^4,d^a=d^2e^4,e^a=d^4e^17,d^b=d^11,e^b=e^11,d^c=d^16e^4,e^c=d^6e^1733 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 14);