Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C43 |
No aliases for this group.
| Fitting | C61×#391 ⋊ C4 |
| Sylow | C61 ⋊ #14378 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6923 |
| commutator, socle | C23×C61 | C23×C4 |
| Fitting | C61×#391 | C4 |
| prime radical, cosocle | C23×D61 | C24 |
| hypercenter | #391 | #6923 |
| hypocenter | C61 | #14378 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #391 | |
1310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,i^a=i^11,c^b=cg,d^b=de,i^h=i^60484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098873);