Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C3×C43×Dic17 |
| derived, Sylow | C17 ⋊ C3×C4×C43 |
| Hall | C3×C17×C43 ⋊ C4 |
| Hall | C17×C43 ⋊ C3×C4 |
| Hall | C3×C17 ⋊ C4×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C43 | D17 |
| commutator, hypocenter | C17 | C3×C4×C43 |
| Frattini | C2 | C3×D17×C43 |
| Fitting, socle | C2×C3×C17×C43 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C3×C43 | |
24 conjugacy classes of subgroups.
2580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C43×Dic17, Dic17×C43⋊C9, C3×Dic17×C43⋊C3, … |
| maximal normal subgroup of | C9×C43×Dic17, Dic17×C43⋊C9, C3×Dic17×C43⋊C3, … |
| maximal quotient of | C9×C43×Dic17, C3×C43×Dic51, C32×C43×Dic17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 4);