Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#72245696 |
6107 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 6107 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72246879, C2×#72246216 |
| maximal normal subgroup of | C2×#72246879, C2×#72246216 |
Past the SmallGroups library coverage — no SmallGroups id.