Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C44 · Schur multiplier (H2) = C46 |
| direct product | C43×Dic61 |
| derived, Sylow | C61 ⋊ C44 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D61 |
| commutator, hypocenter | C61 | C44 |
| Frattini | C24 | C23×D61 |
| Fitting | C2×C43×C61 | C2 |
| socle, prime radical, cosocle | C24×C61 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C43 | |
3966 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, 90634);