Finite Group DatabasebetaFinite Group Databasebeta| order | 7511 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×C37) |
| unambiguous semidirect product | (C29×C37)⋊C7 |
| Fitting, socle, Hall | C29×C37 ⋊ C7 |
| derived, Sylow | C29 ⋊ C7×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C29⋊C7 |
| commutator, hypocenter | C29 | C7×C37 |
| Frattini | C1 | G |
| Fitting, socle | C29×C37 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
407 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37×C29⋊C7, D37×C29⋊C7, C37×D29⋊C7, … |
| maximal normal subgroup of | C2×C37×C29⋊C7, D37×C29⋊C7, C37×D29⋊C7, … |
| maximal quotient of | C2×C37×C29⋊C7, C3×C37×C29⋊C7, C5×C37×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7511, 1);