Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C8×#6923 |
| Fitting | C23×C8×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C23×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #6923 |
| commutator, hypocenter | C61 | C23×C4×C8 |
| Frattini | C4 | C24×#6923 |
| Fitting | C23×C8×C61 | C4 |
| socle | C24×C61 | C42 |
| prime radical | C24×D61 | C2×C4 |
| cosocle | C4×D61 | C25 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C8 | |
4638 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, 1114642);