Finite Group DatabasebetaFinite Group Databasebeta| order | 15596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#14555805 |
| Fitting, socle, derived, Hall | C7×C557 ⋊ C4 |
| Sylow | C557 ⋊ Dic7 |
| Sylow | C7 ⋊ #14555805 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C557 | C4 |
| prime radical, cosocle | C7×D557 | C2 |
| LCS | G ▷ C7×C557 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3899 |
Polycyclic presentation:
2^2,7,557|a^2=b,c^a=c^6,d^a=d^439,d^b=d^556983 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15596, 7);