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 | C2×C4×C5×Dic3 |
| unambiguous semidirect product | (C2×C3)⋊(C42×C5) |
| derived, Sylow | C3 ⋊ C2×C42×C5 |
| Hall | C3×C5 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C5 | D3 |
| commutator, hypocenter | C3 | C2×C42×C5 |
| Frattini | C22 | C22×C5×D3 |
| Fitting | C22×C3×C4×C5 | C2 |
| socle, prime radical | C23×C3×C5 | C22 |
| cosocle | C22×C3 | C23×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C4×C5 | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(4,5)(6,7,8,9)(14,15,16,17,18);(3,4,5)(10,11,12,13);(1,2)240 conjugacy classes — view the full character table.
| maximal subgroup of | #11745967, #11745974, #11745976, … |
| maximal normal subgroup of | #11745967, #11745974, #11745976, … |
| maximal quotient of | C2×C4×C5×C3⋊C8, C2×C5×#803, C4×C5×#208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 801);