Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×#6038 |
| Hall | C32×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C3×D3×D4 |
| Sylow | C32 ⋊ C2×#6038 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D52 |
| commutator, cosocle | C2×C3×C52 | C23×C3 |
| Frattini | C2 | C3×D3×D52 |
| Fitting, socle | C2×C32×C52 | C23 |
| hypocenter | C3×C52 | C2×C3×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3 | |
602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#87886, AGL(1,ℤ/9)×#6038 |
| maximal normal subgroup of | C3×D3×#87886 |
| maximal quotient of | AGL(1,ℤ/9)×#6038 |
Past the SmallGroups library coverage — no SmallGroups id.