Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×D57 |
| Fitting, socle, derived, Hall | C32×C5×C19 ⋊ C22 |
| Hall | C32×C19 ⋊ C2×D5 |
| Hall | C5×C19 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D19 |
| Sylow | C19 ⋊ D3×D15 |
| Sylow | C32 ⋊ D5×D19 |
| Sylow | C5 ⋊ D3×D57 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C19 | C22 |
| LCS | G ▷ C32×C5×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 570 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D57×D75, C5×D15×D57, D57×C3⋊(C5⋊D5), … |
| maximal normal subgroup of | C5×D15×D57, C7×D15×D57, C11×D15×D57 |
| maximal quotient of | D57×D75, C5×D15×D57, D57×C3⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 118);