Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D259 |
| unambiguous semidirect product | (C7×D7)⋊D37 |
| unambiguous semidirect product | (D7×C37)⋊D7 |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C22 |
| Sylow | C72 ⋊ C2×D37 |
| Sylow | C37 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C37 | C22 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
655 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D37, D7×#13095537, D7×#13095538, … |
| maximal normal subgroup of | D7×#13095537, D7×#13095538, #13095535⋊D7, … |
| maximal quotient of | C3×D7×D259, D7×D777, D21×D259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 25);