Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#2617 ⋊ C2 |
| Sylow | C61 ⋊ #34575 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C61×#2617 | C2 |
| hypercenter | #2617 | D61 |
| hypocenter | C61 | #34575 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2617 | |
2794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dh,c^b=ch,i^e=i^601024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 336141);