Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C64 · Schur multiplier (H2) = C4 |
| direct product | C4×#16839481 |
| derived, Sylow | C61 ⋊ C4×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C32 | D61 |
| commutator, hypocenter | C61 | C4×C64 |
| Frattini | C2×C32 | C2×D61 |
| Fitting | C4×C32×C61 | C2 |
| socle, prime radical | C22×C61 | C2×C32 |
| cosocle | C2×C32×C61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C4×C32 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
4096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 57371);