Finite Group DatabasebetaFinite Group Databasebeta| order | 1488 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D8×C31⋊C3 |
| unambiguous semidirect product | (D8×C31)⋊C3 |
| Fitting, Hall | D8×C31 ⋊ C3 |
| Sylow | C31 ⋊ C3×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×C31⋊C3 |
| commutator, cosocle | C4×C31 | C22×C3 |
| Frattini | C4 | C22×C31⋊C3 |
| Fitting | D8×C31 | C3 |
| socle | C2×C31 | C3×D4 |
| hypercenter | D8 | C31⋊C3 |
| hypocenter | C31 | C3×D8 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
91 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1488, 53);