Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C157 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊#10597845 |
| commutator | C4×C157 | C2×C4 |
| Frattini | C4 | C2×#10597845 |
| Fitting | C8×C157 | C4 |
| socle | C2×C157 | C4⋊C4 |
| hypercenter | C8 | #10597845 |
| hypocenter | C157 | #108 |
| LCS | G ▷ C4×C157 ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,157|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^129,f^d=f^156326 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 216);