Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C3×C43 |
| direct product | C42×C3⋊ΓL(1,𝔽16) |
| Fitting | C32×C42×C5 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C43 |
| Sylow | C32 ⋊ C42×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C42×C3⋊Dic3 |
1548 conjugacy classes of subgroups; only the 489 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 489 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×C3⋊D3×AGL(1,𝔽5), #127×C3⋊ΓL(1,𝔽16), #72231684, … |
| maximal normal subgroup of | C42×C3⋊D3×AGL(1,𝔽5), #127×C3⋊ΓL(1,𝔽16), #72231684, … |
Past the SmallGroups library coverage — no SmallGroups id.