Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊((C2×D3)⋊C4) |
| Hall | C3×C5 ⋊ C2×C22⋊C4 |
| Sylow | C5 ⋊ C2×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ C2×C22⋊AGL(1,𝔽5) |
264 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 70 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:
(1,2)(4,5)(6,7)(8,9)(10,11,12,14,13);(3,4,5)(7,9)(11,12,13,14);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | #11751836, #11751841, C4×(C2×D3)⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #11751836, #11751841, C4×(C2×D3)⋊AGL(1,𝔽5), … |
| maximal quotient of | C2×#91151, C2×#91152, #11751703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1000);