Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#10597845 |
| unambiguous semidirect product | D157⋊(C22×C4) |
| Fitting, socle | C23×C157 ⋊ C4 |
| derived, Sylow | C157 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10597845 |
| commutator, hypocenter | C157 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C157 | C4 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 235);