Finite Group DatabasebetaFinite Group Databasebeta| order | 15996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C31×C43 ⋊ C3×C4 |
| Hall | C31×Dic43 ⋊ C3 |
| Hall | #16860688 ⋊ C4 |
| Hall | Dic43 ⋊ C31⋊C3 |
| Sylow | C43 ⋊ C4×C31⋊C3 |
| Sylow | C31 ⋊ (C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22547862 |
| commutator, hypocenter | C31×C43 | C3×C4 |
| Fitting, socle, cosocle | C2×C31×C43 | C2×C3 |
| prime radical | C2×#16860688 | C2 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5332 |
Polycyclic presentation:
2,3,31,43,2|a^2=e,d^a=d^42,c^b=c^25,d^b=d^6486 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15996, 16);