Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D17×D29 |
| unambiguous semidirect product | (C29×D17)⋊(C2×C32) |
| unambiguous semidirect product | (C17×D29)⋊(C2×C32) |
| unambiguous semidirect product | D493⋊(C2×C32) |
| Fitting, socle, Hall | C32×C17×C29 ⋊ C22 |
| derived, Hall | C17×C29 ⋊ C22×C32 |
| Hall | C32×C29 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C32×D17 |
| Sylow | C17 ⋊ C2×C32×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D17×D29 |
| commutator, cosocle, hypocenter | C17×C29 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C29 | C22 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4437 |
1440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 56);