Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #11744621 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Hall | C32×C25 ⋊ C8 |
| Sylow | C25 ⋊ #622 |
| Sylow | C32 ⋊ #6016 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11744621 |
| commutator, hypocenter | C32×C25 | C8 |
| Frattini | C2×C5 | #4380 |
| Fitting | C2×C32×C25 | C4 |
| socle, prime radical | C2×C32×C5 | AGL(1,𝔽5) |
| cosocle | C3⋊Dic75 | C2 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^3,3^2,5^2|a^2=b,b^2=c,f^5=g,d^a=de,e^a=de^2,f^a=f^2g,g^a=g^2,d^b=d^2,e^b=e^2,f^b=f^4g^4,g^b=g^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 65);