Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C24×C3×D5 |
| unambiguous semidirect product | C5⋊(C25×C3) |
| unambiguous semidirect product | (C2×C5)⋊(C24×C3) |
| Fitting, socle | C24×C3×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C25×C3 |
| Hall | C3×C5 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | D5 |
| commutator, cosocle, hypocenter | C5 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C3 | |
1496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 5 generators on 16 points:
(1,2)(3,4)(5,6)(7,8)(9,10,11)(13,14)(15,16);(7,8)(12,13,15,16,14);(5,6);(3,4);(1,2)192 conjugacy classes — view the full character table.
| maximal subgroup of | #11749488, C3×#65244, C3×#65800, … |
| maximal normal subgroup of | #11749488, C3×#65244, C3×#65800, … |
| maximal quotient of | C23×C3×Dic10, C23×C3×C4×D5, C23×C3×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1210);