Finite Group DatabasebetaFinite Group Databasebeta| order | 8436 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×(C37⋊C3)⋊D19 |
| unambiguous semidirect product | (C2×C37⋊C3)⋊D19 |
| Fitting, socle | C2×C19×C37 ⋊ C2×C3 |
| derived, Hall | C19×C37 ⋊ C22×C3 |
| Hall | C2×D703 ⋊ C3 |
| Hall | C19×C37⋊C3 ⋊ C22 |
| Hall | C37⋊C3 ⋊ C2×D19 |
| Sylow | C37 ⋊ C2×C3×D19 |
| Sylow | C19 ⋊ C2×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C37⋊C3)⋊D19 |
| commutator, hypocenter | C19×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C37 | C2×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8436, 48);