Finite Group DatabasebetaFinite Group Databasebeta| order | 15561 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19104440 |
| Fitting, socle | C3×C7×C13×C19 ⋊ C3 |
| derived, Hall | C7×C13×C19 ⋊ C32 |
| Hall | C13×C19 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C19 ⋊ C3×C13⋊C3 |
| Hall | C7×C13 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×#63270 |
| Sylow | C13 ⋊ C3×#87704 |
| Sylow | C7 ⋊ C3×#10625202 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19104440 |
| commutator, cosocle, hypocenter | C7×C13×C19 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5187 |
1737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#23780625, C3×#23780612, C3×#23780599, … |
| maximal normal subgroup of | C3×#23780625, C3×#23780612, C3×#23780599, … |
| maximal quotient of | C2×C3×#19104440 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15561, 38);