Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C79 ⋊ C2 |
| Sylow | C79 ⋊ SD64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1264 |
| commutator | C16×C79 | C22 |
| Frattini | C16 | C2×D79 |
| Fitting | C32×C79 | C2 |
| socle | C2×C79 | D16 |
| hypercenter | C32 | D79 |
| hypocenter | C79 | SD64 |
| LCS | G ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^78,c^b=cd,d^b=de,e^b=ef,g^b=g^781267 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 388);