Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D157⋊C16 |
| derived, Sylow | C157 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #10597845 |
| commutator, hypocenter | C157 | C2×C16 |
| Frattini | C4 | C2×#10597845 |
| Fitting | C8×C157 | C4 |
| socle | C2×C157 | C2×C8 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,157|a^2=c,c^2=d,d^2=e,f^a=f^129,f^b=f^156,f^c=f^156344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 219);