Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C211 · Schur multiplier (H2) = C1 |
| direct product | D25×C211 |
| unambiguous semidirect product | C25⋊(C2×C211) |
| Fitting, Hall | C25×C211 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C211 |
| Frattini | C5 | D5×C211 |
| Fitting | C25×C211 | C2 |
| socle | C5×C211 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C211 | |
12 conjugacy classes of subgroups.
2954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1035×C211, C211⋊#1035, D25×D211, … |
| maximal normal subgroup of | #1035×C211, C211⋊#1035, D25×D211, … |
| maximal quotient of | Dic25×C211, C2×D25×C211, C3×D25×C211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 4);