Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C61 ⋊ #34985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C61×#2308 | C2 |
| prime radical | C23×D4×C61 | C22 |
| hypercenter | #2308 | D61 |
| hypocenter | C61 | #34985 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2308 | |
2866 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=f,c^2=f,b^a=bf,c^a=cg,e^a=eh,c^b=ch,d^b=dh,i^b=i^60,i^c=i^601384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 342158);