Finite Group DatabasebetaFinite Group Databasebeta| order | 8178 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D87 |
| unambiguous semidirect product | C3⋊(C47×D29) |
| unambiguous semidirect product | C29⋊(D3×C47) |
| Fitting, socle, Hall | C3×C29×C47 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C2×C47 |
| Hall | C29×C47 ⋊ D3 |
| Hall | C3×C47 ⋊ D29 |
| Sylow | C29 ⋊ D3×C47 |
| Sylow | C3 ⋊ C47×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D87 |
| commutator, hypocenter | C3×C29 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C47 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
2115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D87, D3×C47×D29, D87⋊D47, … |
| maximal normal subgroup of | D47×D87, D3×C47×D29, D87⋊D47, … |
| maximal quotient of | C47×Dic87, C2×C47×D87, C47×D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8178, 7);