Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C128 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D61⋊C128 |
| derived, Sylow | C61 ⋊ C2×C128 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | #6923 |
| commutator, hypocenter | C61 | C2×C128 |
| Frattini | C32 | C2×#6923 |
| Fitting | C61×C64 | C4 |
| socle | C2×C61 | C2×C64 |
| prime radical | C2×D61 | C64 |
| cosocle | #16839481 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C64 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^11,i^b=i^60,i^c=i^601216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1084871);