Finite Group DatabasebetaFinite Group Databasebeta| order | 15561 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11717941 |
| derived, Hall | C7×C13 ⋊ C9×C19 |
| Hall | C7×C13×C19 ⋊ C9 |
| Hall | C13×C19 ⋊ C7⋊C9 |
| Hall | C7×C19 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C19×C7⋊C9 |
| Sylow | C7 ⋊ C19×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #63270 |
| commutator, hypocenter | C7×C13 | C9×C19 |
| Frattini | C3 | C19×#63270 |
| Fitting, socle, prime radical | C3×C7×C13×C19 | C3 |
| cosocle | C3×C7×C13 | C3×C19 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15561 |
1881 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×#11717941, D19×#11717941, C19×#13109896, … |
| maximal normal subgroup of | C2×C19×#11717941, D19×#11717941, C19×#13109896, … |
| maximal quotient of | C2×C19×#11717941 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15561, 9);