Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D171 |
| unambiguous semidirect product | (C2×C9)⋊(C5×D19) |
| unambiguous semidirect product | (C2×C19)⋊(C5×D9) |
| Fitting | C2×C5×C9×C19 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C22×C5 |
| Hall | C5×C9×C19 ⋊ C22 |
| Hall | C5×C19 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×C5×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D171 |
| commutator, cosocle, hypocenter | C9×C19 | C22×C5 |
| Frattini | C3 | C2×C5×D57 |
| Fitting | C2×C5×C9×C19 | C2 |
| socle | C2×C3×C5×C19 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C2×C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×D171, C5×D5×D171, C2×C52×D171, … |
| maximal normal subgroup of | C2×C25×D171, C2×C52×D171, C2×C5×C7×D171, … |
| maximal quotient of | C2×C25×D171, C5×D5×D171, C2×C52×D171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 38);