Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#15692425 |
| Fitting, Hall | C5×C361 ⋊ C9 |
| derived, Sylow | C361 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #15692425 |
| commutator, hypocenter | C361 | C5×C9 |
| Frattini | C19 | C5×#4296 |
| Fitting | C5×C361 | C9 |
| socle | C5×C19 | #4296 |
| prime radical | C5×C361⋊C3 | C3 |
| cosocle | C361⋊C3 | C3×C5 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C5 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1805 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15692425⋊C2, D5×#15692425, C5⋊(#15692425⋊C2), … |
| maximal normal subgroup of | C5×#15692425⋊C2, D5×#15692425, C5⋊(#15692425⋊C2), … |
| maximal quotient of | C2×C5×#15692425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 4);