Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C73⋊C3)⋊D7) |
| unambiguous semidirect product | (C73⋊C3)⋊D21 |
| Fitting, socle, derived | C3×C7×C73 ⋊ C2×C3 |
| Hall | C3×C7×C73⋊C3 ⋊ C2 |
| Hall | C3×C73⋊C3 ⋊ D7 |
| Hall | C7×C73 ⋊ C3×D3 |
| Sylow | C73 ⋊ C3×D21 |
| Sylow | C7 ⋊ C3⋊(D73⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C73 | C2×C3 |
| LCS | G ▷ C3×C7×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,73|c^a=c^2,d^a=d^6,e^a=e^72,e^b=e^8288 conjugacy classes — view the full character table.
| maximal subgroup of | D21×D73⋊C3, D7×C3⋊(D73⋊C3), D3×(C73⋊C3)⋊D7, … |
| maximal normal subgroup of | D21×D73⋊C3, D7×C3⋊(D73⋊C3), D3×(C73⋊C3)⋊D7, … |
| maximal quotient of | C3⋊#20259490, C2×C3⋊((C73⋊C3)⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 68);