Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×Dic3×AGL(1,𝔽5) |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊(C4×C5) |
| unambiguous semidirect product | ΓL(1,𝔽16)⋊(C4×C5) |
| derived | C3×C5 ⋊ C42×C5 |
| Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×C5×AGL(1,𝔽5) |
126 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 538);