Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C157 ⋊ C2 |
| Sylow | C157 ⋊ #102 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D628 |
| commutator | C4×C157 | C2×C4 |
| Frattini | C2×C4 | C2×D157 |
| Fitting | C2×C8×C157 | C2 |
| socle | C22×C157 | D4 |
| hypercenter | C2×C8 | D157 |
| hypocenter | C157 | #102 |
| LCS | G ▷ C4×C157 ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,157|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^156,c^b=ce,f^b=f^1561262 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 68);