Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic79 |
| commutator | C4×C79 | C42 |
| Frattini | C2×C8 | C2×D79 |
| Fitting | M32×C79 | C2 |
| socle | C2×C79 | #97 |
| hypercenter | M32 | D79 |
| hypocenter | C79 | #347 |
| LCS | G ▷ C4×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ M32 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^78802 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 326);