Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×#168 |
| derived | C5 ⋊ C32×C5×C8 |
| Hall | C32×C52 ⋊ C8 |
| Sylow | C52 ⋊ C32×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4×C5 | D5 |
| commutator, hypocenter | C5 | C32×C5×C8 |
| Frattini | C4 | C32×C5×D5 |
| Fitting | C32×C4×C52 | C2 |
| socle, prime radical | C2×C32×C52 | C4 |
| cosocle | C4×C5 | C2×C32×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C32×C4×C5 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 261);