Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#10597845 |
| unambiguous semidirect product | D157⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#10597845)⋊C22 |
| Fitting | C23×C157 ⋊ C4 |
| Sylow | C157 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#10597845 |
| commutator | C2×C157 | C22×C4 |
| Frattini | C2 | C22×#10597845 |
| Fitting | C23×C157 | C4 |
| socle | C22×C157 | C2×C4 |
| hypercenter | C23 | #10597845 |
| hypocenter | C157 | C2×C22⋊C4 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C23 | |
132 conjugacy classes of subgroups.
332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 223);