Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C73 ⋊ C2×C9 |
| Hall | #17987160 ⋊ C2 |
| Hall | D7×C73 ⋊ C9 |
| Sylow | C73 ⋊ D7⋊C9 |
| Hall | D7 ⋊ #10620321 |
| Sylow | C7 ⋊ C2×#10620321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15690446 |
| commutator, hypocenter | C7×C73 | C2×C9 |
| Fitting, socle | C3×C7×C73 | C2×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,73,3|b^3=e,c^a=c^6,c^b=c^2,d^b=d^64381 conjugacy classes — view the full character table.
| maximal subgroup of | #22604091⋊C2, C2×#22604095 |
| maximal normal subgroup of | #22604091⋊C2, C2×#22604095 |
| maximal quotient of | #32913702, C2×#22604095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 20);