Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×(C5⋊D5)⋊C9 |
| unambiguous semidirect product | (C3×C5⋊D5)⋊C9 |
| derived, Sylow | C52 ⋊ C2×C3×C9 |
| Hall | C3×C52⋊C9 ⋊ C2 |
| Hall | C5⋊D5 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C9 |
| Frattini | C3 | C3×(C5⋊D5)⋊C3 |
| Fitting, socle | C32×C52 | C2×C3 |
| prime radical | C32×C5⋊D5 | C3 |
| cosocle | C3×C52 | C2×C32 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 49);