Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11929639 |
| unambiguous semidirect product | (C2×#11929639)⋊C2 |
| Fitting | C22×C317 ⋊ C4 |
| Sylow | C317 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11929639 |
| commutator, socle | C2×C317 | C2×C4 |
| Fitting | C22×C317 | C4 |
| hypercenter | C22 | #11929639 |
| hypocenter | C317 | C22⋊C4 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C2 ◁ C22 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,317|a^2=d,b^a=bc,e^a=e^203,e^d=e^316326 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 45);