Finite Group DatabasebetaFinite Group Databasebeta| order | 16425 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#10620323 |
| Fitting, Hall | C25×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #10620323 |
| commutator, hypocenter | C73 | C9×C25 |
| Frattini | C5 | C5×#10620323 |
| Fitting | C25×C73 | C9 |
| socle | C5×C73 | C5×C9 |
| prime radical, cosocle | C5×C73⋊C3 | C3×C5 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1825 |
425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#10620323⋊C2, C25⋊(#10620323⋊C2), D25×#10620323, … |
| maximal normal subgroup of | C25×#10620323⋊C2, C25⋊(#10620323⋊C2), D25×#10620323, … |
| maximal quotient of | C2×C25×#10620323 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16425, 4);