Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#10620323⋊C2 |
| unambiguous semidirect product | #10620323⋊(C2×C7) |
| Fitting, socle, Hall | C7×C73 ⋊ C2×C9 |
| derived, Sylow | C73 ⋊ C2×C7×C9 |
| Hall | C7×#10620323 ⋊ C2 |
| Hall | C7×D73 ⋊ C9 |
| Hall | #10620323 ⋊ C2×C7 |
| Hall | D73 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #10620323⋊C2 |
| commutator, hypocenter | C73 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C7×C73 | C2×C9 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14581496, #32913830, D7×#10620323⋊C2, … |
| maximal normal subgroup of | C7×#14581496, #32913830, D7×#10620323⋊C2, … |
| maximal quotient of | C7×#14581484, C2×C7×#10620323⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 26);