Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C19⋊C3)⋊D19) |
| unambiguous semidirect product | (C19⋊C3)⋊D95 |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C3 |
| Hall | C5×C19×C19⋊C3 ⋊ C2 |
| Hall | C5⋊(C19⋊D19) ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ D5 |
| Sylow | C192 ⋊ C3×D5 |
| Sylow | C5 ⋊ (C19⋊C3)⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C192 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|c^a=c^4,d^a=d^18,e^a=e^18,d^b=d^7432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 36);