Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#11710730 |
| Fitting, Sylow | C4×#62817 ⋊ C3 |
| derived | #62817 ⋊ C3×C4 |
30741 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 30741 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#11710730, C4×#72209831, C4×#72209641, … |
| maximal normal subgroup of | C4×#72209831, C4×#72209641, C4×#72209772, … |
| maximal quotient of | AGL(1,𝔽5)×#11710730 |
Past the SmallGroups library coverage — no SmallGroups id.