Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C181 ⋊ C4×C9 |
| Hall | C5×#13108658 ⋊ C4 |
| Hall | Dic905 ⋊ C9 |
| Hall | #13108658 ⋊ Dic5 |
| Sylow | C181 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ #20266783 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(#13108658⋊C2) |
| commutator, hypocenter | C5×C181 | C4×C9 |
| Fitting, socle | C2×C5×C181 | C2×C9 |
| prime radical, cosocle | C2×C5×C181⋊C3 | C2×C3 |
| LCS | G ▷ C5×C181 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,181,2|a^2=f,b^3=c,d^a=d^4,e^a=e^180,e^b=e^39,e^c=e^132172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 78);