Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#11725071 |
| derived, Hall | C43×#89205 ⋊ C2 |
| Hall | C72×C43 ⋊ D9 |
| Hall | #89205 ⋊ D43 |
| Sylow | C72 ⋊ D387 |
| Sylow | C43 ⋊ #11725071 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C43×#89205 | C2 |
| Frattini | C3 | C43⋊#64418 |
| Fitting, socle | C3×C72×C43 | D3 |
| LCS | G ▷ C43×#89205 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2709 |
Polycyclic presentation:
2,3,43,7^2,3|b^3=f^2,b^a=b^2f,c^a=c^42,d^a=d^2e^3,e^a=d^6e^5,f^a=f^2,d^b=d^4e^4,e^b=e^21236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 168);