Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×C22⋊D5 |
| Fitting | C23×C3×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ C22×D4 |
| Sylow | C5 ⋊ C2×D3×D4 |
| Sylow | C3 ⋊ C22×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C23×C3×C5 | C22 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | C22×D4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 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 — 4 generators on 14 points:
(3,4,5)(7,9)(10,11,13,14,12);(6,7)(8,9)(11,12)(13,14);(1,2)(4,5);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3938, D3×#4011, D3×#4013, … |
| maximal normal subgroup of | D3×#3938, D3×#4011, D3×#4013, … |
| maximal quotient of | C2×#91329, C2×#91351, C2×#91352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1123);