Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#14579119 |
| Fitting | C2×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#117 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D79 |
| commutator | C2×C79 | C23×C4 |
| Frattini | C22 | C23×D79 |
| Fitting | C2×C4⋊C4×C79 | C2 |
| socle | C23×C79 | C23 |
| hypercenter | C2×C4⋊C4 | D79 |
| hypocenter | C79 | C2×#117 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 1004);