Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#557 ⋊ C4 |
| Sylow | C61 ⋊ #34337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#6923 |
| commutator, socle | C22×C61 | C24×C4 |
| Fitting | C61×#557 | C4 |
| prime radical, cosocle | C22×D61 | C25 |
| hypercenter | #557 | #6923 |
| hypocenter | C61 | #34337 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #557 | |
2124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=f,c^2=g,d^2=f,e^2=fgh,b^a=bf,c^a=cg,e^a=ef,i^a=i^50,d^b=df,i^e=i^11,i^h=i^60463 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1114448);