Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #339 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22⋊D79 |
| commutator | C4×C79 | C42 |
| Frattini | C22×C4 | C2×D79 |
| Fitting | #117×C79 | C2 |
| socle | C22×C79 | C22⋊C4 |
| hypercenter | #117 | D79 |
| hypocenter | C79 | #339 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #117 | |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^78808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 308);