Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C61 ⋊ #7556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C25 | C22×D61 |
| commutator | C23×C61 | C2×C42 |
| Fitting | C22×#95×C61 | C2 |
| socle, prime radical, cosocle | C25×C61 | C23 |
| hypercenter | C22×#95 | D61 |
| hypocenter | C61 | #7556 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
2582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=h,c^2=d,b^a=bd,c^a=ce,c^b=cf,i^b=i^60,i^c=i^602488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 57493);