Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)×C73⋊C3 ⋊ C2 |
| Hall | D511 ⋊ C32 |
| Sylow | C73 ⋊ C3×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C3×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C2×C32 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,73|d^a=d^6,e^a=e^72,e^b=e^8,d^c=d^281 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D73⋊C3, C2×ΓL(1,𝔽8)⋊(D73⋊C3) |
| maximal normal subgroup of | AGL(1,𝔽7)×D73⋊C3, C2×ΓL(1,𝔽8)⋊(D73⋊C3) |
| maximal quotient of | ΓL(1,𝔽8)⋊(Dic73⋊C3), C2×ΓL(1,𝔽8)⋊(D73⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 31);