Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| isoclinism | isoclinic class of D95 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D95 |
| unambiguous semidirect product | (C2×C5)⋊(C9×D19) |
| Fitting | C2×C5×C9×C19 ⋊ C2 |
| derived, Hall | C5×C19 ⋊ C22×C9 |
| Hall | C5×C9×C19 ⋊ C22 |
| Hall | C9×C19 ⋊ C2×D5 |
| Hall | C5×C9 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×C9×D19 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
882 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×D475, C9×D5×D95, C2×C5×C9×D95, … |
| maximal normal subgroup of | C2×C5×C9×D95, C2×C7×C9×D95, C2×C9×C11×D95 |
| maximal quotient of | C2×C9×D475, C9×D5×D95, C2×C5×C9×D95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 36);