Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C43 |
| direct product | C2×#21454213 |
| Fitting | C22×#127×C61 ⋊ C2 |
| Sylow | C61 ⋊ C2×#2867 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D61 |
| commutator, cosocle | C23×C61 | C25 |
| Frattini | C23 | C24×D61 |
| Fitting | C22×#127×C61 | C2 |
| socle | C24×C61 | C24 |
| hypercenter | C22×#127 | D61 |
| hypocenter | C61 | C2×#2867 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
8094 conjugacy classes of subgroups; only the 1243 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 375661);