Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#72236889 |
| Fitting | C2×#20612 ⋊ D3 |
11118 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 11118 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72241001, C2×#72240998, C2×#72236967 |
| maximal normal subgroup of | C2×#72241001, C2×#72240998, C2×#72236967 |
Past the SmallGroups library coverage — no SmallGroups id.