Finite Group DatabasebetaFinite Group Databasebeta| order | 9198 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C7×C73⋊C3 |
| unambiguous semidirect product | (C2×C73)⋊(C32×C7) |
| unambiguous semidirect product | (C2×C3×C73)⋊(C3×C7) |
| Fitting, socle | C2×C3×C7×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C2×C32×C7 |
| Hall | C2×C7×C73 ⋊ C32 |
| Hall | C7×C73 ⋊ C2×C32 |
| Hall | C2×C73 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | C73⋊C3 |
| commutator, hypocenter | C73 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C3×C7 | |
48 conjugacy classes of subgroups.
1134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic73⋊C3, C3×#20259490, C3×Dic7×C73⋊C3, … |
| maximal normal subgroup of | C3×C7×Dic73⋊C3, C3×#20259490, C3×Dic7×C73⋊C3, … |
| maximal quotient of | C3×C4×C7×C73⋊C3, C22×C3×C7×C73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9198, 70);