Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #23372 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6923 |
| commutator, socle, prime radical | C23×C61 | C23×C4 |
| Fitting | C61×#382 | C4 |
| cosocle | C22×Dic61 | C24 |
| hypercenter | #382 | #6923 |
| hypocenter | C61 | #23372 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #382 | |
584 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 194 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=g,b^2=f,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=defh,i^a=i^11,c^b=cefh,d^b=deh,i^b=i^60,i^d=i^60,i^g=i^60472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1113292);