Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C61 ⋊ #13818 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D61 |
| commutator | C22×C61 | C22×C42 |
| Fitting | C4×#95×C61 | C2 |
| socle, prime radical, cosocle | C24×C61 | C24 |
| hypercenter | C4×#95 | D61 |
| hypocenter | C61 | #13818 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
1690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=h,c^2=eg,d^2=fg,b^a=be,c^a=cf,i^a=i^60,d^b=de2500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 91116);