Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#17987160 |
| derived, Hall | C7×C73 ⋊ C2×C9 |
| Hall | C2×C7×C73 ⋊ C9 |
| Hall | C2×C73 ⋊ C7⋊C9 |
| Sylow | C73 ⋊ C2×C7⋊C9 |
| Hall | C2×C7 ⋊ #10620321 |
| Sylow | C7 ⋊ C2×#10620321 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #13095276 |
| commutator, hypocenter | C7×C73 | C2×C9 |
| Frattini | C3 | C2×#13095276 |
| Fitting, socle | C2×C3×C7×C73 | C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
1038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#17987160, #32913698, #32913702, … |
| maximal normal subgroup of | C4×#17987160, #32913698, #32913702, … |
| maximal quotient of | C4×#17987160, C22×#17987160 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 5);