Finite Group DatabasebetaFinite Group Databasebeta| order | 39732 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#14268588 |
| commutator, hypocenter | C7×C11×C43 | C3×C4 |
| Fitting, socle | C2×C7×C11×C43 | C2×C3 |
| LCS | G ▷ C7×C11×C43 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,43,2|a^2=f,d^a=d^10,e^a=e^42,c^b=c^2,e^b=e^361148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(39732, 40);