Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C42×D5 |
| Fitting | C3×C42×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C3×C42 |
| Hall | C3×C5 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C42 | D5 |
| commutator, hypocenter | C5 | C2×C3×C42 |
| Frattini | C22 | C22×C3×D5 |
| Fitting | C3×C42×C5 | C2 |
| socle | C22×C3×C5 | C23 |
| prime radical | C22×C3×D5 | C22 |
| cosocle | C22×C5 | C23×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C42 | |
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)(14,15,16);(1,2,4,5,3)(10,13,12,11);(6,9,8,7)192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64862, #11746733, #11746868, … |
| maximal normal subgroup of | C3×#64862, #11746733, #11746868, … |
| maximal quotient of | C3×#64937, C3×#64938, C3×D5×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 664);