Finite Group DatabasebetaFinite Group Databasebeta| order | 15596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic557 |
| derived, Sylow | C557 ⋊ C4×C7 |
| Hall | C7×C557 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D557 |
| commutator, hypocenter | C557 | C4×C7 |
| Frattini | C2 | C7×D557 |
| Fitting, socle, prime radical | C2×C7×C557 | C2 |
| cosocle | C2×C557 | C2×C7 |
| LCS | G ▷ C557 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15596 |
3920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15596, 3);