Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #543 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D79 |
| commutator, socle | C22×C79 | C24 |
| Fitting | C2×C22⋊C4×C79 | C2 |
| hypercenter | C2×C22⋊C4 | D79 |
| hypocenter | C79 | #543 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
242 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^78802 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 1175);