Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of #401⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C4×#401⋊C7 |
| unambiguous semidirect product | (C4×#401)⋊C7 |
| Fitting, Sylow | C4×#401 ⋊ C7 |
| derived | #401 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #401⋊C7 |
| commutator, hypocenter | #401 | C4×C7 |
| Frattini, socle | C24 | C2×AGL(1,𝔽8) |
| Fitting | C4×#401 | C7 |
| prime radical | C2×#401⋊C7 | C2 |
| cosocle | C2×#401 | C2×C7 |
| LCS | G ▷ #401 | |
| UCS | C1 ◁ C4 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083475);