Finite Group DatabasebetaFinite Group Databasebeta| order | 15620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #21462835⋊C2 |
| unambiguous semidirect product | #21462841⋊C2 |
| unambiguous semidirect product | #21462847⋊C2 |
| Fitting, socle, derived, Hall | C11×C71 ⋊ C22×C5 |
| Hall | #16840848 ⋊ C22 |
| Hall | D11×D71 ⋊ C5 |
| Sylow | C71 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C71 | C22×C5 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 781 |
Polycyclic presentation:
2^2,5,11,71|e^a=e^70,d^b=d^10,d^c=d^4,e^c=e^5471 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15620, 37);