Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | D43⋊#89205 |
| derived, Hall | C72×C43 ⋊ C2×C9 |
| Hall | C43⋊#89205 ⋊ C2 |
| Hall | C72×D43 ⋊ C9 |
| Hall | D43 ⋊ #89205 |
| Sylow | C72 ⋊ D43⋊C9 |
| Sylow | C43 ⋊ C2×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D43⋊#3862 |
| commutator, hypocenter | C72×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C43 | C2×C3 |
| prime radical | C3×C72×D43 | C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2709 |
Polycyclic presentation:
2,3,7^2,43,3|b^3=f,e^a=e^42,c^b=c^2,d^b=d^4,e^b=e^361143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 157);