Finite Group DatabasebetaFinite Group Databasebeta| order | 32637 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C43 · Schur multiplier (H2) = C1 |
| direct product | C3×C43×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C3×C11×C43) |
| unambiguous semidirect product | (C3×C23)⋊(C11×C43) |
| unambiguous semidirect product | (C3×C23×C43)⋊C11 |
| Fitting, socle, Hall | C3×C23×C43 ⋊ C11 |
| derived, Sylow | C23 ⋊ C3×C11×C43 |
| Hall | C23×C43 ⋊ C3×C11 |
| Hall | C3×C23 ⋊ C11×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C3×C11×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C43 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C43 | |
16 conjugacy classes of subgroups.
1677 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C43×C23⋊C11, C3×D43×C23⋊C11, C3×C43×AGL(1,𝔽23), … |
| maximal normal subgroup of | C2×C3×C43×C23⋊C11, C3×D43×C23⋊C11, C3×C43×AGL(1,𝔽23), … |
| maximal quotient of | C2×C3×C43×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32637, 2);