Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D157⋊M16 |
| Sylow | C157 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#10597845 |
| commutator, socle | C2×C157 | C22×C4 |
| Frattini | C2 | C22×#10597845 |
| Fitting | C2×C4×C157 | C4 |
| hypercenter | C2×C4 | #10597845 |
| hypocenter | C157 | C2×M16 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,157|a^2=d,d^2=e,b^a=be,f^a=f^129,f^c=f^156,f^d=f^156332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 231);