Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×AΓL(1,𝔽25) |
| Fitting, socle | C3×C52 ⋊ ΓL(1,𝔽25) |
| Hall | C3×C52⋊C3 ⋊ M16 |
| Sylow | C52 ⋊ C3×ΓL(1,𝔽25) |
104 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 28 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.
| maximal subgroup of | D3×AΓL(1,𝔽25) |
| maximal normal subgroup of | D3×AΓL(1,𝔽25) |
| automorphism group of | C52⋊C9 |
Past the SmallGroups library coverage — no SmallGroups id.