Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C5 |
| direct product | C3×#10597074 |
| derived | C52⋊C3 ⋊ C3×C8 |
| Hall | C3×C52⋊C3 ⋊ C8 |
| Sylow | C52 ⋊ C3×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #64480 |
| commutator, hypocenter | C52⋊C3 | C3×C8 |
| Frattini | C2 | C3×#64480 |
| Fitting, socle | C2×C3×C52 | Dic3 |
| prime radical | C2×C3×C52⋊C3 | C4 |
| cosocle | #1039⋊C3 | C2×C3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 329);