Finite Group DatabasebetaFinite Group Databasebeta| order | 8650 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C173 · Schur multiplier (H2) = C1 |
| direct product | D25×C173 |
| unambiguous semidirect product | C25⋊(C2×C173) |
| Fitting, Hall | C25×C173 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | D25 |
| commutator, hypocenter | C25 | C2×C173 |
| Frattini | C5 | D5×C173 |
| Fitting | C25×C173 | C2 |
| socle | C5×C173 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C173 | |
12 conjugacy classes of subgroups.
2422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1035×C173, #31772404, D25×D173, … |
| maximal normal subgroup of | #1035×C173, #31772404, D25×D173, … |
| maximal quotient of | Dic25×C173, C2×D25×C173, C3×D25×C173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8650, 2);