Finite Group DatabasebetaFinite Group Databasebeta| order | 11214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1869 |
| unambiguous semidirect product | C7⋊(C3⋊D267) |
| unambiguous semidirect product | C89⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C89 ⋊ C2 |
| Hall | C32×C89 ⋊ D7 |
| Hall | C7×C89 ⋊ C3⋊D3 |
| Sylow | C89 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D89 |
| Sylow | C32 ⋊ D623 |
| Sylow | C7 ⋊ C3⋊D267 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C89 | C2 |
| LCS | G ▷ C32×C7×C89 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,89|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^882805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1869, D21×D267, C3⋊D21×D89, … |
| maximal normal subgroup of | D3×D1869, D21×D267, C3⋊D21×D89, … |
| maximal quotient of | C3⋊Dic1869, C2×C3⋊D1869 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11214, 22);