Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
| direct product | C8×#14519683 |
| derived, Sylow | C61 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C16 | D61 |
| commutator, hypocenter | C61 | C8×C32 |
| Frattini | C4×C16 | C2×D61 |
| Fitting | C8×C16×C61 | C2 |
| socle, prime radical | C22×C61 | C4×C16 |
| cosocle | C4×C16×C61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C8×C16 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
4096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56894);