Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×#2104⋊C7 |
| unambiguous semidirect product | (C2×#2104)⋊C7 |
| Fitting, Sylow | C2×#2104 ⋊ C7 |
| derived | #2104 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22 | #401⋊C7 |
| commutator, cosocle, hypocenter | #2104 | C2×C7 |
| Frattini | C24 | C2×AGL(1,𝔽8) |
| Fitting | C2×#2104 | C7 |
| LCS | G ▷ #2104 | |
| UCS | C1 ◁ C22 | |
81 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
34 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083480);