Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D5×C17 |
| unambiguous semidirect product | C5⋊(C2×C32×C5×C17) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C2 |
| derived | C5 ⋊ C2×C32×C5×C17 |
| Hall | C52×C17 ⋊ C2×C32 |
| Hall | C32×C52 ⋊ C2×C17 |
| Sylow | C52 ⋊ C2×C32×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C17 | D5 |
| commutator, hypocenter | C5 | C2×C32×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C32×C5×C17 | |
120 conjugacy classes of subgroups.
3060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 53);