Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #389 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D79 |
| commutator | C22×C79 | C22×C4 |
| Fitting | C2×C4⋊C4×C79 | C2 |
| socle | C23×C79 | C23 |
| hypercenter | C2×C4⋊C4 | D79 |
| hypocenter | C79 | #389 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
170 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 77 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,b^2=f,c^2=e,b^a=bd,c^a=ce,g^c=g^78808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 444);