Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10620323⋊D7 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C2×C9 |
| Hall | C7×#10620323 ⋊ C2 |
| Hall | D511 ⋊ C9 |
| Hall | #10620323 ⋊ D7 |
| Sylow | C73 ⋊ C9×D7 |
| Sylow | C7 ⋊ #10620323⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C2×C9 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,73|b^3=c,d^a=d^6,e^a=e^72,e^b=e^2,e^c=e^873 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#10620323⋊C2, C2×#10620323⋊D7 |
| maximal normal subgroup of | D7×#10620323⋊C2, C2×#10620323⋊D7 |
| maximal quotient of | #32913770, C2×#10620323⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 36);