Finite Group DatabasebetaFinite Group Databasebeta| order | 6550 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C131 · Schur multiplier (H2) = C1 |
| direct product | D25×C131 |
| unambiguous semidirect product | C25⋊(C2×C131) |
| Fitting, Hall | C25×C131 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | D25 |
| commutator, hypocenter | C25 | C2×C131 |
| Frattini | C5 | D5×C131 |
| Fitting | C25×C131 | C2 |
| socle | C5×C131 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C131 | |
12 conjugacy classes of subgroups.
1834 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1035×C131, C131⋊#1035, D25×D131, … |
| maximal normal subgroup of | #1035×C131, C131⋊#1035, D25×D131, … |
| maximal quotient of | Dic25×C131, C2×D25×C131, C3×D25×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6550, 4);