Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×C5×D3 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| derived, Sylow | C3 ⋊ C23×C4×C5 |
| Hall | C3×C5 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C5 | D3 |
| commutator, hypocenter | C3 | C23×C4×C5 |
| Frattini | C2 | C23×C5×D3 |
| Fitting | C22×C3×C4×C5 | C2 |
| socle | C23×C3×C5 | C22 |
| prime radical | C23×C5×D3 | C2 |
| cosocle | C2×C3 | C24×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C4×C5 | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2)(3,4)(6,7)(12,13,14,15,16);(5,6,7)(8,9,10,11);(3,4);(1,2)240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×D3)⋊#168, #11748346, D3×C22⋊#168, … |
| maximal normal subgroup of | C2×(C2×D3)⋊#168, #11748346, D3×C22⋊#168, … |
| maximal quotient of | C2×C4×C5×Dic6, C2×C42×C5×D3, C2×C5×#872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1151);