Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C8 · Schur multiplier (H2) = C215 |
| direct product | C24×D61⋊C8 |
| unambiguous semidirect product | D61⋊(C24×C8) |
| derived, Sylow | C61 ⋊ C25×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | #6923 |
| commutator, hypocenter | C61 | C25×C8 |
| Frattini | C2 | C25×#6923 |
| Fitting | C24×C4×C61 | C4 |
| socle | C25×C61 | C2×C4 |
| prime radical | C25×D61 | C4 |
| cosocle | Dic61 | C26 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C24×C4 | |
15454 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.
This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 8408 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1116291);