Finite Group DatabasebetaFinite Group Databasebeta| order | 3720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | D4×(C31⋊C3)⋊C5 |
| Fitting, Hall | D4×C31 ⋊ C3×C5 |
| Hall | D4×ΓL(1,𝔽32) ⋊ C3 |
| Hall | D4×C31⋊C3 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C3×D4 |
| Hall | C31⋊C3 ⋊ C5×D4 |
| Sylow | C31 ⋊ C3×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×(C31⋊C3)⋊C5 |
| commutator, socle, cosocle | C2×C31 | C22×C3×C5 |
| Fitting | D4×C31 | C3×C5 |
| hypercenter | D4 | (C31⋊C3)⋊C5 |
| hypocenter | C31 | C3×C5×D4 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ D4 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 124 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽31), S4×(C31⋊C3)⋊C5, C2×D4×(C31⋊C3)⋊C5 |
| maximal normal subgroup of | D4×AGL(1,𝔽31), C2×D4×(C31⋊C3)⋊C5 |
| maximal quotient of | C2×D4×(C31⋊C3)⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.