Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic51 |
| unambiguous semidirect product | C3⋊(C41×Dic17) |
| derived, Hall | C3×C17 ⋊ C4×C41 |
| Hall | C3×C17×C41 ⋊ C4 |
| Hall | C17×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C41 |
| Sylow | C3 ⋊ C41×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D51 |
| commutator, hypocenter | C3×C17 | C4×C41 |
| Frattini | C2 | C41×D51 |
| Fitting, socle | C2×C3×C17×C41 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
2214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×Dic153, C41×C3⋊Dic51, C3×C41×Dic51 |
| maximal normal subgroup of | C3×C41×Dic51 |
| maximal quotient of | C41×Dic153, C41×C3⋊Dic51, C3×C41×Dic51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 7);