Finite Group DatabasebetaFinite Group Databasebeta| order | 8350 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D167 |
| unambiguous semidirect product | C167⋊(C2×C25) |
| Fitting, Hall | C25×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D167 |
| commutator, hypocenter | C167 | C2×C25 |
| Frattini | C5 | C5×D167 |
| Fitting | C25×C167 | C2 |
| socle | C5×C167 | C2×C5 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
2125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D167, C2×C25×D167, C3×C25×D167, … |
| maximal normal subgroup of | D25×D167, C2×C25×D167, C3×C25×D167 |
| maximal quotient of | C25×Dic167, C2×C25×D167, C3×C25×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8350, 3);