Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×C3⋊#1043 |
| Fitting | C3×C52×C22⋊C4 ⋊ C4 |
| Hall | C3×C52 ⋊ C4×C22⋊C4 |
| Sylow | C52 ⋊ Dic3×C22⋊C4 |
| Sylow | C3 ⋊ C22⋊C4×#1043 |
2064 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 265 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 600 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊C4×#1043 |
| maximal normal subgroup of | D3×C22⋊C4×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.