Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic259 |
| unambiguous semidirect product | C7⋊(C7×Dic37) |
| derived | C7×C37 ⋊ C4×C7 |
| Hall | C72×C37 ⋊ C4 |
| Sylow | C72 ⋊ Dic37 |
| Sylow | C37 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D259 |
| commutator, hypocenter | C7×C37 | C4×C7 |
| Frattini | C2 | C7×D259 |
| Fitting, socle | C2×C72×C37 | C2 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
1834 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#15690926, C7×#15690927, C7×ΓL(1,𝔽8)⋊Dic37, … |
| maximal normal subgroup of | C7×#15690926, C7×#15690927, C7×ΓL(1,𝔽8)⋊Dic37, … |
| maximal quotient of | C7×Dic777, C3×C7×Dic259, C7×Dic1295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 15);