Finite Group DatabasebetaFinite Group Databasebeta| order | 8436 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#14523722 |
| Fitting, Hall | C4×C19×C37 ⋊ C3 |
| derived, Hall | C19×C37 ⋊ C3×C4 |
| Hall | C4×C37 ⋊ C19⋊C3 |
| Hall | C4×C19 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ C4×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14523722 |
| commutator, hypocenter | C19×C37 | C3×C4 |
| Frattini | C2 | C2×#14523722 |
| Fitting | C4×C19×C37 | C3 |
| socle | C2×C19×C37 | C2×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
948 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8436, 4);