Finite Group DatabasebetaFinite Group Databasebeta| order | 3720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C3⋊(D31⋊C5) |
| Fitting, socle | C22×C3×C31 ⋊ C2×C5 |
| derived, Hall | C3×C31 ⋊ C23×C5 |
| Hall | C22×D93 ⋊ C5 |
| Hall | C3×ΓL(1,𝔽32) ⋊ C23 |
| Hall | ΓL(1,𝔽32) ⋊ C22×D3 |
| Sylow | C31 ⋊ C22×C5×D3 |
| Sylow | C3 ⋊ C22×D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(D31⋊C5) |
| commutator, cosocle, hypocenter | C3×C31 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C31 | C2×C5 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C22 | |
128 conjugacy classes of subgroups.
96 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊AGL(1,𝔽31), C22×D3×D31⋊C5, C2×C4×C3⋊(D31⋊C5), … |
| maximal normal subgroup of | C22×C3⋊AGL(1,𝔽31), C22×D3×D31⋊C5, C2×C4×C3⋊(D31⋊C5), … |
| maximal quotient of | C2×C4×C3⋊(D31⋊C5) |
Past the SmallGroups library coverage — no SmallGroups id.