Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×Dic51 |
| unambiguous semidirect product | C3⋊(C3×C13×Dic17) |
| derived | C3×C17 ⋊ C3×C4×C13 |
| Hall | C32×C13×C17 ⋊ C4 |
| Hall | C13×C17 ⋊ C3×Dic3 |
| Hall | C32×C17 ⋊ C4×C13 |
| Hall | C32×C13 ⋊ Dic17 |
| Sylow | C17 ⋊ C3×Dic3×C13 |
| Sylow | C32 ⋊ C13×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | D51 |
| commutator, hypocenter | C3×C17 | C3×C4×C13 |
| Frattini | C2 | C3×C13×D51 |
| Fitting, socle | C2×C32×C13×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C3×C13 | |
56 conjugacy classes of subgroups.
2106 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 66);