Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C82×C61 ⋊ C4 |
| Sylow | C61 ⋊ #7846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×#6923 |
| commutator, socle | C22×C61 | C43 |
| Fitting | C82×C61 | C4 |
| prime radical | C22×D61 | C2×C42 |
| cosocle | C42×D61 | C23 |
| hypercenter | C82 | #6923 |
| hypocenter | C61 | #7846 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C82 | |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=cg,c^b=ch,i^c=i^11,i^f=i^601072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1085534);