Finite Group DatabasebetaFinite Group Databasebeta| order | 11550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | D21×C11⋊C25 |
| unambiguous semidirect product | C3⋊(D7×C11⋊C25) |
| unambiguous semidirect product | C7⋊(D3×C11⋊C25) |
| unambiguous semidirect product | (C11×D21)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D21×C11⋊C5 |
| commutator, hypocenter | C3×C7×C11 | C2×C25 |
| Fitting, socle, cosocle | C3×C5×C7×C11 | C2×C5 |
| prime radical | C5×C11×D21 | C5 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
| maximal subgroup of | D21×D11⋊C25, D21⋊(D11⋊C25), D3×D7×C11⋊C25, … |
| maximal normal subgroup of | D21×D11⋊C25, D21⋊(D11⋊C25), D3×D7×C11⋊C25, … |
| maximal quotient of | Dic21×C11⋊C25, C2×D21×C11⋊C25, D63×C11⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11550, 25);