Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | C22×#16840475 |
| Fitting | C22×#117×C61 ⋊ C2 |
| Sylow | C61 ⋊ C22×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D61 |
| commutator, cosocle | C22×C61 | C26 |
| Frattini | C22 | C25×D61 |
| Fitting | C22×#117×C61 | C2 |
| socle | C24×C61 | C24 |
| hypercenter | C22×#117 | D61 |
| hypocenter | C61 | C22×#555 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×#117 | |
8710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
2500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1076587);