Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×#5950 |
| Fitting, Sylow | C2×C4×#585 ⋊ C3 |
19897 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 19897 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72245747, C2×#72245579, C2×#72245692, … |
| maximal normal subgroup of | C2×#72245747, C2×#72245579, C2×#72245692, … |
Past the SmallGroups library coverage — no SmallGroups id.