Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C61 ⋊ #17308 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D61 |
| commutator, socle, prime radical, cosocle | C24×C61 | C24 |
| Fitting | C61×#1446 | C2 |
| hypercenter | #1446 | D61 |
| hypocenter | C61 | #17308 |
| LCS | G ▷ C24×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
1034 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 243 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=efg,b^2=efh,c^2=g,d^2=efg,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=def,i^b=i^60,d^c=de,i^c=i^60,i^d=i^601366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 135130);