Finite Group DatabasebetaFinite Group Databasebeta| order | 32180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C1609 ⋊ C4 |
| Sylow | C1609 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #20264457 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C1609 | C4 |
| prime radical, cosocle | D8045 | C2 |
| LCS | G ▷ C5×C1609 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8045 |
Polycyclic presentation:
2^2,5,1609|a^2=b,c^a=c^2,d^a=d^1086,c^b=c^4,d^b=d^16082015 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32180, 8);