Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C317 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D317 |
| commutator | C4×C317 | C22 |
| Frattini | C4 | C2×D317 |
| Fitting | D4×C317 | C2 |
| socle | C2×C317 | D4 |
| hypercenter | D4 | D317 |
| hypocenter | C317 | SD16 |
| LCS | G ▷ C4×C317 ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,317|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^316,c^b=cd797 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 28);