Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #510 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D79 |
| commutator | C8×C79 | C23 |
| Frattini | C8 | C22×D79 |
| Fitting | Q32×C79 | C2 |
| socle | C2×C79 | C2×D8 |
| hypercenter | Q32 | D79 |
| hypocenter | C79 | #510 |
| LCS | G ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^78,d^b=de,e^b=ef,g^c=g^78445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 991);