Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C3×C4⋊C4) |
| Fitting | C2×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ C2×C3×C4⋊C4 |
184 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4,5)(6,7,8,9)(10,11,12,14,13);(7,9)(11,12,13,14);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #11746528, #11746529, #11746534, … |
| maximal normal subgroup of | #11746528, #11746529, #11746534, … |
| maximal quotient of | C3×D5⋊(C4⋊C8), C3×#65681, C3×#65682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1051);