Finite Group DatabasebetaFinite Group Databasebeta| order | 32637 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C11×C23×C43⋊C3 |
| unambiguous semidirect product | C43⋊(C3×C11×C23) |
| unambiguous semidirect product | (C11×C43)⋊(C3×C23) |
| unambiguous semidirect product | (C11×C23×C43)⋊C3 |
| Fitting, socle, Hall | C11×C23×C43 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C11×C23 |
| Hall | C23×C43 ⋊ C3×C11 |
| Hall | C11×C43 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C23 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C3×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C11×C23 | |
16 conjugacy classes of subgroups.
4301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C23×C43⋊C3, C11×C23×D43⋊C3, C11×D23×C43⋊C3, … |
| maximal normal subgroup of | C2×C11×C23×C43⋊C3, C11×C23×D43⋊C3, C11×D23×C43⋊C3, … |
| maximal quotient of | C2×C11×C23×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32637, 3);