Finite Group DatabasebetaFinite Group Databasebeta| order | 10656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | D4×AGL(1,𝔽37) |
| Fitting | D4×C37 ⋊ C4×C9 |
| Hall | D4×#3866 ⋊ C9 |
| Hall | #66526 ⋊ C4×D4 |
| Sylow | C37 ⋊ C4×D4×C9 |
282 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 148 |
185 conjugacy classes — view the full character table.
| maximal subgroup of | S4×AGL(1,𝔽37) |
| holomorph of | C4×C37 |
Past the SmallGroups library coverage — no SmallGroups id.