Finite Group DatabasebetaFinite Group Databasebeta| order | 8946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1491 |
| unambiguous semidirect product | C7⋊(C3⋊D213) |
| unambiguous semidirect product | C71⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C71 ⋊ C2 |
| Hall | C32×C71 ⋊ D7 |
| Hall | C7×C71 ⋊ C3⋊D3 |
| Sylow | C71 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D71 |
| Sylow | C32 ⋊ D497 |
| Sylow | C7 ⋊ C3⋊D213 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C71 | C2 |
| LCS | G ▷ C32×C7×C71 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,71|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^702238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D21×D71, D7×C3⋊D213, C3⋊D3×D497, … |
| maximal normal subgroup of | C3⋊D21×D71, D7×C3⋊D213, C3⋊D3×D497, … |
| maximal quotient of | C3⋊Dic1491, C2×C3⋊D1491 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8946, 42);