Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊((C19⋊C3)⋊D19)) |
| unambiguous semidirect product | C5⋊(C3⋊((C19⋊C3)⋊D19)) |
| unambiguous semidirect product | (C19⋊C3)⋊D285 |
| Fitting, socle, derived | C3×C5×C192 ⋊ C2×C3 |
| Hall | C3×C5×C19×C19⋊C3 ⋊ C2 |
| Hall | C3×C19×C19⋊C3 ⋊ D5 |
| Hall | C5×C192 ⋊ C3×D3 |
| Sylow | C192 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3⋊((C19⋊C3)⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C192 | C2×C3 |
| LCS | G ▷ C3×C5×C192 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
Polycyclic presentation:
2,3^2,5,19^2|c^a=c^2,d^a=d^4,e^a=e^18,f^a=f^18,e^b=e^71287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 193);