Finite Group DatabasebetaFinite Group Databasebeta| order | 36876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×(C439⋊C3)⋊C4 |
| unambiguous semidirect product | (C439⋊C3)⋊(C4×C7) |
| unambiguous semidirect product | Dic439⋊(C3×C7) |
| derived, Sylow | C439 ⋊ C3×C4×C7 |
| Hall | C7×Dic439 ⋊ C3 |
| Hall | C7×C439⋊C3 ⋊ C4 |
| Hall | C7×C439 ⋊ C3×C4 |
| Hall | Dic439 ⋊ C3×C7 |
| Hall | C439⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D439⋊C3 |
| commutator, hypocenter | C439 | C3×C4×C7 |
| Frattini | C2 | C7×D439⋊C3 |
| Fitting, socle | C2×C7×C439 | C2×C3 |
| prime radical | C2×C7×C439⋊C3 | C2 |
| cosocle | C2×C439 | C2×C3×C7 |
| LCS | G ▷ C439 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12292 |
1106 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36876, 13);