Finite Group DatabasebetaFinite Group Databasebeta| order | 17532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#17983938⋊C2 |
| unambiguous semidirect product | #17983938⋊C22 |
| unambiguous semidirect product | (C2×#17983938)⋊C2 |
| derived, Sylow | C487 ⋊ C22×C9 |
| Hall | #17983938 ⋊ C22 |
| Hall | C2×D487 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D487⋊C3 |
| commutator, hypocenter | C487 | C22×C9 |
| Frattini | C3 | C2×D487⋊C3 |
| Fitting, socle | C2×C3×C487 | C2×C3 |
| prime radical | C2×C3×D487 | C3 |
| cosocle | C3×C487 | C22×C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8766 |
522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17532, 8);