Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D57 |
| unambiguous semidirect product | (C3×D5)⋊(C3×D19) |
| Fitting, socle, Hall | C32×C5×C19 ⋊ C22 |
| derived | C3×C5×C19 ⋊ C22×C3 |
| Hall | C32×C19 ⋊ C2×D5 |
| Hall | C5×C19 ⋊ C2×C3×D3 |
| Hall | C32×C5 ⋊ C2×D19 |
| Sylow | C19 ⋊ C3×D3×D5 |
| Sylow | C32 ⋊ D5×D19 |
| Sylow | C5 ⋊ C2×C3×D57 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D57 |
| commutator, cosocle, hypocenter | C3×C5×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C19 | C22 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 570 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D25×D57, C3×C5×D5×D57, C3×C5⋊D5×D57, … |
| maximal normal subgroup of | C3×C5×D5×D57, C3×C7×D5×D57, C3×D5×C11×D57 |
| maximal quotient of | C3×D25×D57, C3×C5×D5×D57, C3×C5⋊D5×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 101);