Finite Group DatabasebetaFinite Group Databasebeta| order | 15652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C7)⋊#261 |
| unambiguous semidirect product | (C43⋊#261)⋊C7 |
| Fitting, socle, derived, Hall | C13×C43 ⋊ C4×C7 |
| Hall | C13×C43⋊C7 ⋊ C4 |
| Hall | C43⋊#261 ⋊ C7 |
| Hall | C43⋊C7 ⋊ #261 |
| Sylow | C43 ⋊ C7×#261 |
| Sylow | C13 ⋊ Dic43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C43 | C4×C7 |
| prime radical | D13×C43⋊C7 | C2 |
| cosocle | D13×C43 | C2×C7 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 559 |
Polycyclic presentation:
2,7,2,13,43|a^2=c,d^a=d^5,e^a=e^42,e^b=e^41,d^c=d^1273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15652, 14);