Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D32⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D32⋊D5 |
| unambiguous semidirect product | D32⋊(C3×D5) |
| Fitting, socle, Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ C3×GO+(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D32⋊D5 |
| commutator, cosocle | C5×C3⋊D3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C33×C5 | D4 |
| hypocenter | C32×C5 | C3×D4 |
| LCS | G ▷ C5×C3⋊D3 ▷ C32×C5 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×GO+(4,𝔽2), C2×C3×D32⋊D5 |
| maximal normal subgroup of | C3×D5×GO+(4,𝔽2), C2×C3×D32⋊D5 |
| maximal quotient of | C2×C3×D32⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 521);