Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14524206⋊C5 |
| unambiguous semidirect product | ((C19⋊D19)⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C192 ⋊ C2×C3×C5 |
| Hall | #11762245⋊C5 ⋊ C2 |
| Hall | (C19⋊D19)⋊C5 ⋊ C3 |
| Hall | #14524206 ⋊ C5 |
| Hall | C192⋊C5 ⋊ C2×C3 |
| Hall | #11762245 ⋊ C2×C5 |
| Hall | C19⋊D19 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|d^a=d^18,e^a=e^18,d^b=d^11,e^b=e^11,d^c=d^12e^8,e^c=d^14e^1142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 15);