Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C37) |
| derived, Sylow | C49 ⋊ C4×C37 |
| Hall | C37×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D49 |
| commutator, hypocenter | C49 | C4×C37 |
| Frattini | C2×C7 | D7×C37 |
| Fitting | C2×C37×C49 | C2 |
| socle | C2×C7×C37 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C37 | |
18 conjugacy classes of subgroups.
1924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37⋊C3×Dic49, C37×(C49⋊C3)⋊C4, #36344157, … |
| maximal normal subgroup of | C37⋊C3×Dic49, C37×(C49⋊C3)⋊C4, #36344157, … |
| maximal quotient of | C3×C37×Dic49, C37×Dic147, C5×C37×Dic49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 2);