Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D79 |
| commutator, socle | C22×C79 | C22×C4 |
| Fitting | C4⋊C8×C79 | C2 |
| hypercenter | C4⋊C8 | D79 |
| hypocenter | C79 | #446 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,79|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^78,g^c=g^78808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 678);