Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #14268403 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52 ⋊ C8 |
| Sylow | C52 ⋊ AGL(1,𝔽9) |
| Sylow | C32 ⋊ #6033 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C8 |
| prime radical | C52×C3⋊D3 | C4 |
| cosocle | #11744710 | C2 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
Polycyclic presentation:
2^3,3^2,5^2|a^2=b,b^2=c,d^a=e,e^a=de^2,f^a=f^2,g^a=g^2,d^b=de^2,e^b=d^2e^2,f^b=f^4,g^b=g^4,d^c=d^2,e^c=e^245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 597);