Finite Group DatabasebetaFinite Group Databasebeta| order | 15620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×#16840847 |
| Fitting, Hall | C4×C11×C71 ⋊ C5 |
| derived, Hall | C11×C71 ⋊ C4×C5 |
| Hall | C4×C71 ⋊ C11⋊C5 |
| Sylow | C71 ⋊ C4×C11⋊C5 |
| Hall | C4×C11 ⋊ C71⋊C5 |
| Sylow | C11 ⋊ C4×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16840847 |
| commutator, hypocenter | C11×C71 | C4×C5 |
| Frattini | C2 | C2×#16840847 |
| Fitting | C4×C11×C71 | C5 |
| socle, cosocle | C2×C11×C71 | C2×C5 |
| prime radical | C2×#16840847 | C2 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3124 |
644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15620, 7);