Finite Group DatabasebetaFinite Group Databasebeta| order | 7510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D751 |
| Fitting, socle, Hall | C5×C751 ⋊ C2 |
| derived, Sylow | C751 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D751 |
| commutator, hypocenter | C751 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C751 | C2 |
| LCS | G ▷ C751 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
1885 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D751, C2×C5×D751, C3×C5×D751, … |
| maximal normal subgroup of | D5×D751, C2×C5×D751, C3×C5×D751, … |
| maximal quotient of | C5×Dic751, C2×C5×D751, C3×C5×D751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7510, 4);