Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×C4×D5 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C23×C3×C4 |
| Hall | C3×C5 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | D5 |
| commutator, hypocenter | C5 | C23×C3×C4 |
| Frattini | C2 | C23×C3×D5 |
| Fitting | C22×C3×C4×C5 | C2 |
| socle | C23×C3×C5 | C22 |
| prime radical | C23×C3×D5 | C2 |
| cosocle | C2×C5 | C24×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C3×C4 | |
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)(5,6,7)(13,14)(15,16);(8,9,10,11)(12,13,15,16,14);(3,4);(1,2)192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#90955, #11748341, D5×#830, … |
| maximal normal subgroup of | C2×#90955, #11748341, D5×#830, … |
| maximal quotient of | C2×C3×C4×Dic10, C2×C3×C42×D5, C2×C3×#4018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1136);