Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×Dic3×AGL(1,𝔽5) |
| derived, Hall | C3×C5 ⋊ C2×C42 |
| Sylow | C5 ⋊ C2×C4×Dic3 |
| Sylow | C3 ⋊ C2×C4×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C2×C42 |
| Frattini | C2 | C2×D3×AGL(1,𝔽5) |
| Fitting, socle | C22×C3×C5 | C2×C4 |
| prime radical | C22×C3×D5 | C22 |
| cosocle | C2×C3×D5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22 | |
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 94 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)(11,12,13,14);(1,2)(4,5)(6,7,8,9)(10,11,12,14,13);(1,2)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 998);