Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #463 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D79 |
| commutator | C2×C4×C79 | C23 |
| Frattini | C2×C4 | C22×D79 |
| Fitting | C2×D8×C79 | C2 |
| socle | C22×C79 | C2×D4 |
| hypercenter | C2×D8 | D79 |
| hypocenter | C79 | #463 |
| LCS | G ▷ C2×C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,79|b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^78,e^c=ef565 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 762);