Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D3×D5 |
| unambiguous semidirect product | (C5×D3)⋊C24 |
| unambiguous semidirect product | (C3×D5)⋊C24 |
| unambiguous semidirect product | D15⋊C24 |
| Fitting, socle | C23×C3×C5 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C25 |
| Sylow | C5 ⋊ C24×D3 |
| Sylow | C3 ⋊ C24×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D5 |
| commutator, cosocle, hypocenter | C3×C5 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C5 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23 | |
1496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 5 generators on 14 points:
(1,2)(3,4)(5,6)(7,8,9)(11,12)(13,14);(8,9)(10,11,13,14,12);(5,6);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #11748940, #11752025, D3×D5×C22⋊C4, … |
| maximal normal subgroup of | #11748940, #11752025, D3×D5×C22⋊C4, … |
| maximal quotient of | C22×D5×Dic6, C22×#6765, C22×#6766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1207);