Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C61 ⋊ #36701 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, prime radical, cosocle | C23×C61 | C25 |
| Fitting | C61×#2845 | C2 |
| hypercenter | #2845 | D61 |
| hypocenter | C61 | #36701 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
1304 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=h,c^2=f,d^2=f,e^2=g,b^a=bf,c^a=cg,d^a=dh,i^a=i^60,c^b=ch,d^c=dfh,i^c=i^60,i^e=i^60832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 376293);