Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C44 · Schur multiplier (H2) = C46 |
| direct product | C43×#6923 |
| Fitting | C43×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C44 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #6923 |
| commutator, hypocenter | C61 | C44 |
| Frattini | C23 | C23×#6923 |
| Fitting | C43×C61 | C4 |
| socle | C23×C61 | C23×C4 |
| prime radical, cosocle | C23×D61 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C43 | |
3966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098151);