Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#10597845 |
| commutator, socle | C2×C157 | C22×C4 |
| Fitting | Q8×C157 | C4 |
| hypercenter | Q8 | #10597845 |
| hypocenter | C157 | #131 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,157|a^2=d,d^2=e,f^a=f^129,c^b=ce,f^b=f^156,f^c=f^156,f^d=f^156215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 234);