Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×(C3⋊D3)⋊D5 |
| unambiguous semidirect product | D15⋊(C32×D3) |
| Fitting, socle, Hall | C34×C5 ⋊ C22 |
| derived | C32×C5 ⋊ C22×C32 |
| Sylow | C34 ⋊ C2×D5 |
| Sylow | C5 ⋊ C32×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C3⋊D3)⋊D5 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C32 | |
448 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 448);