Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C73 ⋊ C2×C9 |
| Hall | #17987164 ⋊ C2 |
| Hall | C7×D73 ⋊ C9 |
| Hall | D73 ⋊ C7⋊C9 |
| Sylow | C73 ⋊ C2×C7⋊C9 |
| 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,e^a=e^72,d^b=d^2,e^b=e^4,e^c=e^6458 conjugacy classes — view the full character table.
| maximal subgroup of | #32913822, #22604103⋊C2, #32913828, … |
| maximal normal subgroup of | #32913822, #22604103⋊C2, #32913828, … |
| maximal quotient of | #32913768, C2×#22604109 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 34);