Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C3×C25) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C25) |
| unambiguous semidirect product | (C25×D49)⋊C3 |
| Fitting, Hall | C25×C49 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C3×C25 |
| Hall | C25×C49⋊C3 ⋊ C2 |
| Hall | C25×D49 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C2×C25 |
| Hall | D49 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D49⋊C3 |
| commutator, hypocenter | C49 | C2×C3×C25 |
| Frattini, socle | C5×C7 | C5×AGL(1,𝔽7) |
| Fitting | C25×C49 | C2×C3 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D49⋊C3, C2×C25×D49⋊C3, C3×C25×D49⋊C3, … |
| maximal normal subgroup of | D25×D49⋊C3, C2×C25×D49⋊C3, C3×C25×D49⋊C3 |
| maximal quotient of | C25×(C49⋊C3)⋊C4, C2×C25×D49⋊C3, C25×D49⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 2);