Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20266599⋊C5 |
| Fitting, socle, derived, Sylow | C192 ⋊ C2×C5×C9 |
| Hall | #15692433⋊C5 ⋊ C2 |
| Hall | #20266599 ⋊ C5 |
| Hall | (C19⋊D19)⋊C5 ⋊ C9 |
| Hall | #15692433 ⋊ C2×C5 |
| Hall | C192⋊C5 ⋊ C2×C9 |
| Hall | C19⋊D19 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C192 | C2×C5×C9 |
| prime radical | #14524206⋊C5 | C3 |
| cosocle | #11762245 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 95 |
Polycyclic presentation:
2,3,5,3,19^2|b^3=d,e^a=e^18,f^a=f^18,e^b=e^5,f^b=f^5,e^c=e^5f^15,f^c=e^8f^9,e^d=e^11,f^d=f^1194 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 82);