Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | D5×SL(2,ℤ/4) |
| derived | C5×A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×S4 |
| commutator, hypocenter | C5×A4 | C2×C4 |
| Fitting, socle | C23×C5 | C2×D3 |
| prime radical | C2×D5×A4 | C2 |
| cosocle | C2×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,4)(5,6,8,7)(9,10,12,13,11);(6,7,8)(10,11)(12,13)40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 979);