Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C61×#401 ⋊ C4 |
| Sylow | C61 ⋊ #14333 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6923 |
| commutator, socle | C23×C61 | C23×C4 |
| Fitting | C61×#401 | C4 |
| prime radical, cosocle | C23×D61 | C24 |
| hypercenter | #401 | #6923 |
| hypocenter | C61 | #14333 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #401 | |
1094 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=f,c^2=e,d^2=fgh,b^a=be,c^a=cf,i^a=i^50,c^b=cg,d^c=de,i^d=i^11,i^h=i^60394 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098828);