Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C42 |
| direct product | C2×#72213771 |
| Fitting, Sylow | C2×#6342426 ⋊ C3 |
41060 conjugacy classes of subgroups; only the 369 normal subgroups are shown.
This group has 41060 conjugacy classes of subgroups — too many to draw. Only its 369 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213802, C2×#72214051 |
| maximal normal subgroup of | C2×#72213802, C2×#72214051 |
Past the SmallGroups library coverage — no SmallGroups id.