Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C79 ⋊ C2 |
| Sylow | C79 ⋊ #576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D316 |
| commutator | C4×C79 | C24 |
| Frattini | C4 | C23×D79 |
| Fitting | #131×C79 | C2 |
| socle | C2×C79 | C22×D4 |
| hypercenter | #131 | D79 |
| hypocenter | C79 | #576 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
268 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|e^2=f,b^a=be,e^a=ef,g^a=g^78,e^b=ef,g^b=g^78,d^c=df802 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 1354);