Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#3866 |
| Fitting, derived, Hall | C37×C49 ⋊ C4 |
| Sylow | C49 ⋊ #3866 |
| Sylow | C37 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C37×C49 | C4 |
| Frattini | C7 | C7⋊#3866 |
| socle | C7×C37 | Dic7 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,37,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^31,e^a=e^6,d^b=d^36493 conjugacy classes — view the full character table.
| maximal subgroup of | #36344174, #36344175, (C49⋊C3)⋊#3866, … |
| maximal normal subgroup of | #36344174, #36344175, (C49⋊C3)⋊#3866, … |
| maximal quotient of | C3×C49⋊#3866, C3⋊(C49⋊#3866), C5×C49⋊#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 7);