Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D49 |
| unambiguous semidirect product | (C37×D49)⋊C2 |
| unambiguous semidirect product | (C49×D37)⋊C2 |
| unambiguous semidirect product | D1813⋊C2 |
| Fitting, derived, Hall | C37×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C37×C49 | C22 |
| Frattini | C7 | D7×D37 |
| socle | C7×C37 | C2×D7 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
520 conjugacy classes — view the full character table.
| maximal subgroup of | #24925914⋊C2, #24925915⋊C2, D37×D49⋊C3, … |
| maximal normal subgroup of | #24925914⋊C2, #24925915⋊C2, D37×D49⋊C3, … |
| maximal quotient of | C3×D37×D49, D37×D147, D49×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 8);