Finite Group DatabasebetaFinite Group Databasebeta| order | 11638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C11⋊(C23⋊D23) |
| unambiguous semidirect product | C23⋊D253 |
| Fitting, socle, derived, Hall | C11×C232 ⋊ C2 |
| Sylow | C232 ⋊ D11 |
| Sylow | C11 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C232 | C2 |
| LCS | G ▷ C11×C232 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,23^2|b^a=b^10,c^a=c^22,d^a=d^222911 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11638, 35);