Finite Group DatabasebetaFinite Group Databasebeta| order | 37716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic449⋊C7) |
| unambiguous semidirect product | Dic1347⋊C7 |
| derived, Hall | C3×C449 ⋊ C4×C7 |
| Hall | C3×C449⋊C7 ⋊ C4 |
| Hall | Dic1347 ⋊ C7 |
| Hall | C449⋊C7 ⋊ Dic3 |
| Sylow | C449 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ Dic449⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D449⋊C7) |
| commutator, hypocenter | C3×C449 | C4×C7 |
| Fitting, socle, cosocle | C2×C3×C449 | C2×C7 |
| prime radical | C2×C3×C449⋊C7 | C2 |
| LCS | G ▷ C3×C449 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5388 |
Polycyclic presentation:
2,3,7,449,2|a^2=e,b^a=b^2,d^a=d^448,d^c=d^324234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37716, 13);