Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D317⋊C8 |
| derived, Sylow | C317 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11929639 |
| commutator, hypocenter | C317 | C2×C8 |
| Frattini | C2 | C2×#11929639 |
| Fitting | C4×C317 | C4 |
| socle | C2×C317 | C2×C4 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,317|a^2=c,c^2=d,e^a=e^203,e^b=e^316,e^c=e^316332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 48);