Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D79)⋊C8 |
| Fitting | C22⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D79 |
| commutator | C2×C79 | C22×C8 |
| Fitting | C22⋊C8×C79 | C2 |
| socle | C22×C79 | C22×C4 |
| hypercenter | C22⋊C8 | D79 |
| hypocenter | C79 | C8×D4 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 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=e,c^2=e,e^2=f,b^a=bd,g^c=g^78820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 612);