Finite Group DatabasebetaFinite Group Databasebeta| order | 8436 |
| automorphism | Aut(G) order 5466528 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2109 |
| unambiguous semidirect product | C3⋊Dic703 |
| unambiguous semidirect product | C19⋊Dic111 |
| derived, Hall | C3×C19×C37 ⋊ C4 |
| Hall | C19×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ Dic19 |
| Hall | C3×C19 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic57 |
| Sylow | C19 ⋊ Dic111 |
| Sylow | C3 ⋊ Dic703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2109 |
| commutator, hypocenter | C3×C19×C37 | C4 |
| Fitting, socle | C2×C3×C19×C37 | C2 |
| LCS | G ▷ C3×C19×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,37,2|a^2=e,b^a=b^2,c^a=c^18,d^a=d^362112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic4218, Dic14763 |
| maximal normal subgroup of | Dic4218 |
| maximal quotient of | Dic14763 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8436, 12);