Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C256 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C128 | D61 |
| commutator, hypocenter | C61 | C256 |
| Fitting, cosocle | C61×C128 | C2 |
| socle, prime radical | C2×C61 | C128 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C128 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^604096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56093);