Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C4 |
| direct product | C23×#14519774 |
| Fitting | C23×C42×C61 ⋊ C2 |
| Sylow | C61 ⋊ C23×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D61 |
| commutator, cosocle | C22×C61 | C26 |
| Frattini | C22 | C25×D61 |
| Fitting | C23×C42×C61 | C2 |
| socle | C25×C61 | C23 |
| hypercenter | C23×C42 | D61 |
| hypocenter | C61 | C23×#127 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C25 ◁ C23×C42 | |
24030 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
3952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1076255);