Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | D4×C3⋊#1044 |
| Fitting | C3×C52×D4 ⋊ C4 |
| Hall | C3×C52 ⋊ C4×D4 |
| Sylow | C52 ⋊ D4×Dic3 |
| Sylow | C3 ⋊ D4×#1044 |
484 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D5⋊ΓL(1,𝔽16), #72259540, #72259676, … |
| maximal normal subgroup of | D4×D5⋊ΓL(1,𝔽16), #72259540, #72259676, … |
Past the SmallGroups library coverage — no SmallGroups id.