Finite Group DatabasebetaFinite Group Databasebeta| order | 1488 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C16×C31⋊C3 |
| unambiguous semidirect product | (C16×C31)⋊C3 |
| Fitting, Hall | C16×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C16 |
| Frattini | C8 | C2×C31⋊C3 |
| Fitting | C16×C31 | C3 |
| socle | C2×C31 | C3×C8 |
| prime radical | C2×C31⋊C3 | C8 |
| cosocle | C8×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C16 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1488, 2);