Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic57 |
| unambiguous semidirect product | C3⋊(C3×C5×Dic19) |
| derived | C3×C19 ⋊ C3×C4×C5 |
| Hall | C32×C5×C19 ⋊ C4 |
| Hall | C32×C19 ⋊ C4×C5 |
| Hall | C5×C19 ⋊ C3×Dic3 |
| Hall | C32×C5 ⋊ Dic19 |
| Sylow | C19 ⋊ C3×C5×Dic3 |
| Sylow | C32 ⋊ C5×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D57 |
| commutator, hypocenter | C3×C19 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D57 |
| Fitting, socle, prime radical | C2×C32×C5×C19 | C2 |
| cosocle | C2×C3×C19 | C2×C3×C5 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C3×C5 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1140 |
900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C25×Dic57, C3×C52×Dic57, C3×C5×Dic285, … |
| maximal normal subgroup of | C3×C25×Dic57, C3×C52×Dic57, C3×C5×C7×Dic57, … |
| maximal quotient of | C3×C25×Dic57, C3×C52×Dic57, C3×C5×Dic285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 58);