Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C61 ⋊ #14720 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D61 |
| commutator, socle, cosocle | C24×C61 | C24 |
| Fitting | C2×C61×#385 | C2 |
| prime radical | C25×C61 | C23 |
| hypercenter | C2×#385 | D61 |
| hypocenter | C61 | #14720 |
| LCS | G ▷ C24×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C2×#385 | |
2494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^b=i^601744 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 100985);