Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #137×C79 ⋊ C2 |
| Sylow | C79 ⋊ #456 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14579129 |
| commutator | C2×C4×C79 | C23 |
| Frattini | C2×C4 | C22×D79 |
| Fitting | #137×C79 | C2 |
| socle | C2×C79 | #120 |
| hypercenter | #137 | D79 |
| hypocenter | C79 | #456 |
| LCS | G ▷ C2×C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,79|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,d^c=df,g^c=g^78445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 730);