Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C4×2−1+4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #62805 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D61 |
| commutator, socle, cosocle | C22×C61 | C26 |
| Frattini | C22 | C25×D61 |
| Fitting | C4×2−1+4×C61 | C2 |
| hypercenter | C4×2−1+4 | D61 |
| hypocenter | C61 | #62805 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×2−1+4 | |
7104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,e^2=h,f^2=g,b^a=bg,c^a=ch,e^a=eh,i^b=i^60,d^c=dh2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1078021);