Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#72236914 |
8852 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 8852 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240995, C2×#72240992, C2×#72240979 |
| maximal normal subgroup of | C2×#72240995, C2×#72240992, C2×#72240979 |
Past the SmallGroups library coverage — no SmallGroups id.