Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C22×D5×A4 |
| unambiguous semidirect product | C5⋊(C23×A4) |
| unambiguous semidirect product | (C2×C5)⋊(C22×A4) |
| Fitting, socle | C24×C5 ⋊ C2×C3 |
| derived | C22×C5 ⋊ C23×C3 |
| Hall | C24×D5 ⋊ C3 |
| Sylow | C5 ⋊ C23×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×A4 |
| commutator, cosocle, hypocenter | C22×C5 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C5 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C22 | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2)(3,4)(6,7,8)(10,11)(12,13);(3,4)(5,8)(6,7)(9,10,12,13,11);(1,2)64 conjugacy classes — view the full character table.
| maximal subgroup of | #11751639, A4×#685, #11756729, … |
| maximal normal subgroup of | #11751639, A4×#685, #11756729, … |
| maximal quotient of | C2×A4×Dic10, C2×C4×D5×A4, C2×A4×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1202);