Finite Group DatabasebetaFinite Group Databasebeta| order | 5628 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#13064105 |
| Fitting, socle, derived, Hall | C22×C7×C67 ⋊ C3 |
| Hall | C7×C67 ⋊ A4 |
| Hall | C22×C67 ⋊ ΓL(1,𝔽8) |
| Sylow | C67 ⋊ C22⋊ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C67⋊C3 |
| Sylow | C7 ⋊ C22⋊(C67⋊C3) |
| Sylow | C22 ⋊ #13064105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C7×C67 | C3 |
| LCS | G ▷ C22×C7×C67 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,7,67|b^a=c,c^a=bc,d^a=d^2,e^a=e^37628 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5628, 57);