Finite Group DatabasebetaFinite Group Databasebeta| order | 17532 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#17983940 |
| Fitting, Hall | C4×C487 ⋊ C9 |
| derived, Sylow | C487 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #17983940 |
| commutator, hypocenter | C487 | C4×C9 |
| Frattini | C2 | C2×#17983940 |
| Fitting | C4×C487 | C9 |
| socle | C2×C487 | C2×C9 |
| prime radical, cosocle | C2×C487⋊C3 | C2×C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1948 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17532, 18);