Finite Group DatabasebetaFinite Group Databasebeta| order | 1488 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊C16 |
| unambiguous semidirect product | (C31⋊C16)⋊C3 |
| derived, Sylow | C31 ⋊ C3×C16 |
| Hall | C31⋊C16 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D31⋊C3 |
| commutator, hypocenter | C31 | C3×C16 |
| Fitting, cosocle | C8×C31 | C2×C3 |
| socle | C2×C31 | C3×C8 |
| prime radical | C2×C31⋊C3 | C8 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2,3,2^3,31|a^2=c,c^2=d,d^2=e,f^a=f^30,f^b=f^2588 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1488, 1);