Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×AΓL(1,𝔽25) |
| Fitting, socle | C3×C52 ⋊ C2×ΓL(1,𝔽25) |
| Hall | C3×C52⋊C3 ⋊ C2×M16 |
| Sylow | C52 ⋊ D3×ΓL(1,𝔽25) |
346 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 75 |
60 conjugacy classes — view the full character table.
| automorphism group of | C3×C52⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.