Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic51 |
| unambiguous semidirect product | C3⋊(C43×Dic17) |
| derived, Hall | C3×C17 ⋊ C4×C43 |
| Hall | C3×C17×C43 ⋊ C4 |
| Hall | C17×C43 ⋊ Dic3 |
| Hall | C3×C43 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C43 |
| Sylow | C3 ⋊ C43×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D51 |
| commutator, hypocenter | C3×C17 | C4×C43 |
| Frattini | C2 | C43×D51 |
| Fitting, socle | C2×C3×C17×C43 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C43 | |
24 conjugacy classes of subgroups.
2322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×Dic153, C43⋊C3×Dic51, C43×C3⋊Dic51, … |
| maximal normal subgroup of | C43⋊C3×Dic51, C3×C43×Dic51 |
| maximal quotient of | C43×Dic153, C43×C3⋊Dic51, C3×C43×Dic51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 8);