Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C192 ⋊ C9×D5 |
| derived, Hall | C192⋊C5 ⋊ C2×C9 |
| Hall | #15692433⋊C5 ⋊ C2 |
| Hall | #16813380 ⋊ C9 |
| Hall | #15692433 ⋊ D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C192⋊C5 | C2×C9 |
| Fitting, socle | C192 | C9×D5 |
| prime radical | #16813380⋊C3 | C3 |
| cosocle | #11762245⋊C5 | C2×C3 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 95 |
Polycyclic presentation:
2,3^2,5,19^2|b^3=c,d^a=d^4,e^a=ef^4,f^a=f^18,e^b=e^5,f^b=f^5,e^c=e^11,f^c=f^11,e^d=e^17f^3,f^d=e^2f^643 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 81);