Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C16 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×#16840648 |
| derived, Sylow | C61 ⋊ C22×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #6923 |
| commutator, hypocenter | C61 | C22×C4×C16 |
| Frattini | C2×C4 | C23×#6923 |
| Fitting | C23×C8×C61 | C4 |
| socle, prime radical | C24×C61 | C2×C8 |
| cosocle | C2×#92418 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C8 | |
1022 conjugacy classes of subgroups; only the 680 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 680 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15616 |
1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1113360);