Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C3×A4×#1044 |
| Fitting, socle | C22×C3×C52 ⋊ C3×C4 |
| derived | C22×C52 ⋊ C32×C4 |
| Hall | C22×#1044 ⋊ C32 |
| Sylow | C52 ⋊ C3×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×#1044 |
| commutator, hypocenter | C22×C52 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C3×C4 |
| prime radical | C3×A4×C5⋊D5 | C2 |
| cosocle | C22×C5⋊D5 | C2×C32 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C3 | |
264 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | A42×#1044, C3×A4×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C3×A4×D5⋊AGL(1,𝔽5) |
| maximal quotient of | A42×#1044 |
Past the SmallGroups library coverage — no SmallGroups id.