Finite Group DatabasebetaFinite Group Databasebeta| order | 1488 |
| isoclinism | isoclinic class of D93 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C31⋊C16) |
| unambiguous semidirect product | C31⋊(C3⋊C16) |
| derived, Hall | C3×C31 ⋊ C16 |
| Sylow | C31 ⋊ C3⋊C16 |
| Sylow | C3 ⋊ C31⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D93 |
| commutator, hypocenter | C3×C31 | C16 |
| Fitting, cosocle | C3×C8×C31 | C2 |
| socle, prime radical | C2×C3×C31 | C8 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 1488 |
Polycyclic presentation:
2^4,3,31|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^30384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1488, 5);