Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D3×D5 |
| Fitting | C2×C3×C4×C5 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C23×C4 |
| Sylow | C5 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C22×C4×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D5 |
| commutator, hypocenter | C3×C5 | C23×C4 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C2×C3×C4×C5 | C22 |
| socle | C22×C3×C5 | C23 |
| prime radical | C22×D3×D5 | C2 |
| cosocle | C2×C3×C5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 | |
472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 4 generators on 14 points:
(1,2)(3,4,5)(11,12)(13,14);(4,5)(10,11,13,14,12);(6,7,8,9);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(C2×D3)⋊C8, D3×#3952, #11748100, … |
| maximal normal subgroup of | D5×(C2×D3)⋊C8, D3×#3952, #11748100, … |
| maximal quotient of | #11752460, C4×D5×Dic6, #11752516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1086);