Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊(C5⋊(C19⋊D19)) |
| unambiguous semidirect product | C5⋊(C3⋊(C19⋊D19)) |
| unambiguous semidirect product | C19⋊D285 |
| Fitting, socle, derived, Hall | C3×C5×C192 ⋊ C2 |
| Hall | C5×C192 ⋊ D3 |
| Hall | C3×C192 ⋊ D5 |
| Sylow | C192 ⋊ D15 |
| Hall | C3×C5 ⋊ C19⋊D19 |
| Sylow | C5 ⋊ C3⋊(C19⋊D19) |
| Sylow | C3 ⋊ C5⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C192 | C2 |
| LCS | G ▷ C3×C5×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,19^2|b^a=b^2,c^a=c^4,d^a=d^18,e^a=e^182709 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D285, D15×C19⋊D19, D57×D95, … |
| maximal normal subgroup of | D19×D285, D15×C19⋊D19, D57×D95, … |
| maximal quotient of | C3⋊(C19⋊Dic95), C2×C3⋊(C5⋊(C19⋊D19)), C5⋊(C9⋊(C19⋊D19)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 45);