Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×#121×C61 ⋊ C2 |
| Sylow | C61 ⋊ #36706 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C22×#121×C61 | C2 |
| hypercenter | C22×#121 | D61 |
| hypocenter | C61 | #36706 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×#121 | |
3038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^60,c^b=ch,d^b=dfh1732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 376360);