Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C3⋊C16 |
| unambiguous semidirect product | (C2×C3)⋊(C5×C16) |
| derived, Sylow | C3 ⋊ C2×C5×C16 |
| Hall | C3×C5 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C8 | D3 |
| commutator, hypocenter | C3 | C2×C5×C16 |
| Frattini | C8 | C2×C5×D3 |
| Fitting | C2×C3×C5×C8 | C2 |
| socle, prime radical | C22×C3×C5 | C8 |
| cosocle | C3×C8 | C22×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C8 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2)(4,5)(6,7,8,9,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(1,2)(3,4,5)240 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×C3⋊C16, #11745872, #11745873, … |
| maximal normal subgroup of | Dic5×C3⋊C16, #11745872, #11745873, … |
| maximal quotient of | C4×C5×C3⋊C16, C5×C4⋊(C3⋊C16), C2×C5×C3⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 130);