Finite Group DatabasebetaFinite Group Databasebeta| order | 8450 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D25 |
| unambiguous semidirect product | C25⋊(C2×C132) |
| Fitting, Hall | C132×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D25 |
| commutator, hypocenter | C25 | C2×C132 |
| Frattini | C5 | D5×C132 |
| Fitting | C132×C25 | C2 |
| socle | C5×C132 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C132 | |
96 conjugacy classes of subgroups.
2366 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C132×#1035, C13×#13049906, #30683396, … |
| maximal normal subgroup of | C132×#1035, C13×#13049906, #30683396, … |
| maximal quotient of | C132×Dic25, C2×C132×D25, C3×C132×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8450, 14);