Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#64480⋊C2 |
| Fitting, socle | C3×C52 ⋊ C2×C4×D3 |
| derived, Hall | C3×C52⋊C3 ⋊ C22×C4 |
| Sylow | C52 ⋊ C4×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C52⋊C3 | C22×C4 |
| Fitting, socle | C3×C52 | C2×C4×D3 |
| prime radical | D3×#3874⋊C2 | C2 |
| cosocle | C3×(C5⋊D5)⋊C3 | C23 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 | |
340 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 45 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΓL(1,𝔽25) |
| maximal normal subgroup of | D3×AΓL(1,𝔽25) |
Past the SmallGroups library coverage — no SmallGroups id.