Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×#4296 |
| Fitting, socle, Hall | C5×C192 ⋊ C9 |
| derived | C19 ⋊ C5×C9×C19 |
| Sylow | C192 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | #4296 |
| commutator, hypocenter | C19 | C5×C9×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C9 |
| prime radical | C5×C19×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C3×C5×C19 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C19 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
1045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C19×AGL(1,𝔽19), C5×#4296⋊D19, C5×D19×#4296, … |
| maximal normal subgroup of | C5×C19×AGL(1,𝔽19), C5×#4296⋊D19, C5×D19×#4296, … |
| maximal quotient of | C2×C5×C19×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 15);