Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#11715850 |
| Fitting | C22×C4×H(5,𝔽2) ⋊ D3 |
| derived | C22⋊#997 ⋊ C2×C4 |
18020 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 18020 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#11715850, C4×#72209653, C2×C4×#11715850 |
| maximal normal subgroup of | C4×#72209653, C2×C4×#11715850 |
| maximal quotient of | C4×#72209641, C4×#72209772, AGL(1,𝔽5)×#11715850, … |
Past the SmallGroups library coverage — no SmallGroups id.