Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14579180 |
| Fitting | C2×D8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D79 |
| commutator | C4×C79 | C24 |
| Frattini | C4 | C23×D79 |
| Fitting | C2×D8×C79 | C2 |
| socle | C22×C79 | C2×D4 |
| hypercenter | C2×D8 | D79 |
| hypocenter | C79 | C2×#135 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
266 conjugacy classes of subgroups.
574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 1328);