Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| isoclinism | isoclinic class of C3⋊(D19⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| Fitting | C3×C19×C25 ⋊ C2×C3 |
| derived | C3×C19 ⋊ C2×C3×C25 |
| Hall | C3×C25×C19⋊C3 ⋊ C2 |
| Hall | C19×C25 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×C25 |
| Sylow | C19 ⋊ C3×D3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C3⋊(D19⋊C3) |
| commutator, hypocenter | C3×C19 | C2×C3×C25 |
| Frattini | C5 | C5×C3⋊(D19⋊C3) |
| Fitting | C3×C19×C25 | C2×C3 |
| socle | C3×C5×C19 | C2×C3×C5 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C25 | |
54 conjugacy classes of subgroups.
450 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C25×D19⋊C3, D25×C3⋊(D19⋊C3), D75⋊(D19⋊C3), … |
| maximal normal subgroup of | D3×C25×D19⋊C3, D25×C3⋊(D19⋊C3), D75⋊(D19⋊C3), … |
| maximal quotient of | C25×C3⋊((C19⋊C3)⋊C4), C2×C25×C3⋊(D19⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 22);