Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic317 |
| Sylow | C317 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D317 |
| commutator | C2×C317 | C2×C4 |
| Fitting | C2×C4×C317 | C2 |
| socle | C22×C317 | C22 |
| hypercenter | C2×C4 | D317 |
| hypocenter | C317 | C4⋊C4 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,317|a^2=d,b^2=c,b^a=bc,e^a=e^3161274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 20);