Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×AΣL(1,𝔽64) |
| Fitting, Sylow | C4×#2846 ⋊ C3 |
10809 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 10809 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AΣL(1,𝔽64), C4×#11713200, C4×#72209831, … |
| maximal normal subgroup of | C4×#11713200, C4×D4×#120⋊C3 |
| maximal quotient of | AGL(1,𝔽5)×AΣL(1,𝔽64), C4×#72215851, #72341987 |
Past the SmallGroups library coverage — no SmallGroups id.