Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#14579085 |
| Sylow | C79 ⋊ C2×#103 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊D79 |
| commutator | C4×C79 | C22×C4 |
| Frattini | C2×C4 | C22×D79 |
| Fitting | C22×Q8×C79 | C2 |
| socle | C23×C79 | D4 |
| hypercenter | C22×Q8 | D79 |
| hypocenter | C79 | C2×#103 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q8 | |
162 conjugacy classes of subgroups.
808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 540);