Finite Group DatabasebetaFinite Group Databasebeta| order | 11214 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×D89 |
| unambiguous semidirect product | C89⋊(C2×C32×C7) |
| Fitting, socle, Hall | C32×C7×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C32×C7 |
| Hall | C32×C89 ⋊ C2×C7 |
| Hall | C7×C89 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | D89 |
| commutator, cosocle, hypocenter | C89 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C89 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C32×C7 | |
48 conjugacy classes of subgroups.
2898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×#67063, C32×C7⋊#67063, C32×D7×D89, … |
| maximal normal subgroup of | C32×C7×#67063, C32×C7⋊#67063, C32×D7×D89, … |
| maximal quotient of | C32×C7×Dic89, C2×C32×C7×D89 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11214, 32);