Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C61×#3444 ⋊ C2 |
| Sylow | C61 ⋊ #412 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C23×D61 |
| commutator, socle, cosocle | C22×C61 | C26 |
| Frattini | C22 | C25×D61 |
| Fitting | C61×#3444 | C2 |
| hypercenter | #3444 | D61 |
| hypocenter | C61 | #412 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ #3444 | |
7812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|e^2=h,f^2=g,b^a=bg,c^a=ch,d^c=dh,i^d=i^601780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1076676);