Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C37 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D7×C37 |
| unambiguous semidirect product | C7⋊(C22×C7×C37) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C7×C37) |
| Fitting, socle | C2×C72×C37 ⋊ C2 |
| derived | C7 ⋊ C22×C7×C37 |
| Hall | C72×C37 ⋊ C22 |
| Sylow | C72 ⋊ C22×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C37 | D7 |
| commutator, hypocenter | C7 | C22×C7×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C7×C37 | |
52 conjugacy classes of subgroups.
2590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 33);