Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C61×C64 ⋊ C4 |
| Sylow | C61 ⋊ #7510 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×#6923 |
| commutator, socle | C2×C61 | C4×C32 |
| Fitting | C61×C64 | C4 |
| prime radical | C2×D61 | C2×C32 |
| cosocle | C32×D61 | C22 |
| hypercenter | C64 | #6923 |
| hypocenter | C61 | #7510 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C32 ◁ C64 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^b=i^11,i^d=i^601120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1084787);