Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×C13×D17 |
| unambiguous semidirect product | C17⋊(C22×C9×C13) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C9×C13) |
| Fitting | C2×C9×C13×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C22×C9×C13 |
| Hall | C9×C13×C17 ⋊ C22 |
| Hall | C13×C17 ⋊ C22×C9 |
| Hall | C9×C17 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9×C13 | D17 |
| commutator, hypocenter | C17 | C22×C9×C13 |
| Frattini | C3 | C2×C3×C13×D17 |
| Fitting | C2×C9×C13×C17 | C2 |
| socle | C2×C3×C13×C17 | C2×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C9×C13 | |
60 conjugacy classes of subgroups.
2340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 46);