Finite Group DatabasebetaFinite Group Databasebeta| order | 8450 |
| isoclinism | isoclinic class of D169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D169 |
| unambiguous semidirect product | C169⋊(C2×C25) |
| Fitting, Hall | C25×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D169 |
| commutator, hypocenter | C169 | C2×C25 |
| Frattini, socle | C5×C13 | C5×D13 |
| Fitting | C25×C169 | C2 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
2150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#10621721, #30683331, D25×D169, … |
| maximal normal subgroup of | C25×#10621721, #30683331, D25×D169, … |
| maximal quotient of | C25×Dic169, C2×C25×D169, C3×C25×D169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8450, 3);