Finite Group DatabasebetaFinite Group Databasebeta| order | 32180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C1609 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C1609 |
| Fitting, socle, Hall | C5×C1609 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C1609 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1609 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C1609 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1609 | C4 |
| prime radical | D5×C1609 | C2 |
| cosocle | D5 | C2×C1609 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C1609 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8045 |
8045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32180, 7);