Finite Group DatabasebetaFinite Group Databasebeta| order | 8436 |
| automorphism | Aut(G) order 5466528 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4218 |
| direct product | C2×D2109 |
| unambiguous semidirect product | (C2×C3)⋊D703 |
| unambiguous semidirect product | (C2×C19)⋊D111 |
| unambiguous semidirect product | (C2×C37)⋊D57 |
| Fitting, socle | C2×C3×C19×C37 ⋊ C2 |
| derived, Hall | C3×C19×C37 ⋊ C22 |
| Hall | C19×C37 ⋊ C2×D3 |
| Hall | C3×C37 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D57 |
| Sylow | C19 ⋊ C2×D111 |
| Sylow | C3 ⋊ C2×D703 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2109 |
| commutator, hypocenter | C3×C19×C37 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C19×C37 | C2 |
| LCS | G ▷ C3×C19×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8436, C2×D14763 |
| maximal normal subgroup of | D8436 |
| maximal quotient of | D8436, Dic4218, C2×D14763 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8436, 70);