Finite Group DatabasebetaFinite Group Databasebeta| order | 9218 |
| automorphism | Aut(G) order 19265620 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4609 |
| unambiguous semidirect product | C11⋊D419 |
| unambiguous semidirect product | C419⋊D11 |
| Fitting, socle, derived, Hall | C11×C419 ⋊ C2 |
| Sylow | C419 ⋊ D11 |
| Sylow | C11 ⋊ D419 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C419 | C2 |
| LCS | G ▷ C11×C419 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,419|b^a=b^10,c^a=c^4182306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D419, C2×D4609, C3×D4609, … |
| maximal normal subgroup of | D11×D419, C2×D4609, C3×D4609 |
| maximal quotient of | Dic4609, C2×D4609, C3×D4609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9218, 5);