Finite Group DatabasebetaFinite Group Databasebeta| order | 17732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D403 |
| unambiguous semidirect product | (C13×D11)⋊D31 |
| unambiguous semidirect product | (D11×C31)⋊D13 |
| Fitting, socle, derived, Hall | C11×C13×C31 ⋊ C22 |
| Hall | C13×C31 ⋊ C2×D11 |
| Hall | C11×C31 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D31 |
| Sylow | C31 ⋊ D11×D13 |
| Sylow | C13 ⋊ D11×D31 |
| Sylow | C11 ⋊ C2×D403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C31 | C22 |
| LCS | G ▷ C11×C13×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4433 |
1421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17732, 19);