Finite Group DatabasebetaFinite Group Databasebeta| order | 7502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D341 |
| unambiguous semidirect product | C11⋊(C11×D31) |
| unambiguous semidirect product | C31⋊(C11×D11) |
| Fitting, socle, Hall | C112×C31 ⋊ C2 |
| derived | C11×C31 ⋊ C2×C11 |
| Sylow | C112 ⋊ D31 |
| Sylow | C31 ⋊ C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D341 |
| commutator, hypocenter | C11×C31 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C31 | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C11 | |
26 conjugacy classes of subgroups.
1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D31, D11×D341, (C11⋊D11)⋊D31, … |
| maximal normal subgroup of | C11×D11×D31, D11×D341, (C11⋊D11)⋊D31, … |
| maximal quotient of | C11×Dic341, C2×C11×D341, C3×C11×D341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7502, 8);