Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×#10620323 |
| Fitting, socle, Hall | C2×C7×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C2×C7×C9 |
| Hall | C7×C73 ⋊ C2×C9 |
| Hall | C2×C73 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #10620323 |
| commutator, hypocenter | C73 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C73 | C9 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14581484, #32913770, Dic7×#10620323, … |
| maximal normal subgroup of | C7×#14581484, #32913770, Dic7×#10620323, … |
| maximal quotient of | C4×C7×#10620323, C22×C7×#10620323 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 38);