Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×C8×D5 |
| Fitting | C3×C5×C8 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C22×C8 |
| Sylow | C5 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×C8×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D3×D5 |
| commutator, hypocenter | C3×C5 | C22×C8 |
| Frattini | C4 | C2×D3×D5 |
| Fitting | C3×C5×C8 | C22 |
| socle | C2×C3×C5 | C22×C4 |
| prime radical | C2×D3×D5 | C4 |
| cosocle | C3×C4×C5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C8 | |
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3)(4,5)(6,7,8);(1,2,4,5,3)(7,8);(9,10,11,13,12,14,15,16)96 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×C16, D5×#798, D3×#3930, … |
| maximal normal subgroup of | D3×D5×C16, D5×#798, D3×#3930, … |
| maximal quotient of | D3×D5×C16, D5×#798, D3×#3930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 319);