Finite Group DatabasebetaFinite Group Databasebeta| order | 37716 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic449⋊C7 |
| unambiguous semidirect product | Dic449⋊(C3×C7) |
| unambiguous semidirect product | (C3×Dic449)⋊C7 |
| derived, Sylow | C449 ⋊ C3×C4×C7 |
| Hall | C3×C449⋊C7 ⋊ C4 |
| Hall | C3×Dic449 ⋊ C7 |
| Hall | C449⋊C7 ⋊ C3×C4 |
| Hall | Dic449 ⋊ C3×C7 |
| Hall | C3×C449 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D449⋊C7 |
| commutator, hypocenter | C449 | C3×C4×C7 |
| Frattini | C2 | C3×D449⋊C7 |
| Fitting, socle | C2×C3×C449 | C2×C7 |
| prime radical | C2×C3×C449⋊C7 | C2 |
| cosocle | C2×C449 | C2×C3×C7 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5388 |
276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37716, 11);