Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#10597845 |
| unambiguous semidirect product | D157⋊C42 |
| Fitting | C2×C4×C157 ⋊ C4 |
| derived, Sylow | C157 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #10597845 |
| commutator, hypocenter | C157 | C2×C42 |
| Frattini | C2 | C22×#10597845 |
| Fitting | C2×C4×C157 | C4 |
| socle | C22×C157 | C2×C4 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 222);