Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×C5×D3 |
| Fitting | C3×C42×C5 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C42×C5 |
| Hall | C3×C5 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42×C5 | D3 |
| commutator, hypocenter | C3 | C2×C42×C5 |
| Frattini | C22 | C22×C5×D3 |
| Fitting | C3×C42×C5 | C2 |
| socle | C22×C3×C5 | C23 |
| prime radical | C22×C5×D3 | C22 |
| cosocle | C22×C3 | C23×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C42×C5 | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3)(4,5,6,7,8);(1,2,3)(13,14,15,16);(9,10,11,12)240 conjugacy classes — view the full character table.
| maximal subgroup of | #11746853, #11746875, #11746876, … |
| maximal normal subgroup of | #11746853, #11746875, #11746876, … |
| maximal quotient of | C5×#4648, C5×#4649, C5×D3×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 750);