Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#72227957 |
77983 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 77983 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #72268037 |
| maximal normal subgroup of | #72268037 |
Past the SmallGroups library coverage — no SmallGroups id.