Finite Group DatabasebetaFinite Group Databasebeta| order | 9374 |
| automorphism | Aut(G) order 21260232 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4687 |
| unambiguous semidirect product | C43⋊D109 |
| unambiguous semidirect product | C109⋊D43 |
| Fitting, socle, derived, Hall | C43×C109 ⋊ C2 |
| Sylow | C109 ⋊ D43 |
| Sylow | C43 ⋊ D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C109 | C2 |
| LCS | G ▷ C43×C109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,43,109|b^a=b^42,c^a=c^1082345 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D109, C2×D4687, C3×D4687, … |
| maximal normal subgroup of | D43×D109, C2×D4687, C3×D4687, … |
| maximal quotient of | Dic4687, C2×D4687, C3×D4687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9374, 3);