Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C16 · Schur multiplier (H2) = C1 |
| direct product | C16×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×C16)⋊C7 |
| Fitting, Sylow | C23×C16 ⋊ C7 |
| derived | C23 ⋊ C7×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | AGL(1,𝔽8) |
| commutator, hypocenter | C23 | C7×C16 |
| Frattini | C8 | C2×AGL(1,𝔽8) |
| Fitting | C23×C16 | C7 |
| socle | C24 | C7×C8 |
| prime radical | C2×AGL(1,𝔽8) | C8 |
| cosocle | C23×C8 | C2×C7 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C16 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C32×AGL(1,𝔽8), C2×C16×AGL(1,𝔽8), M32×AGL(1,𝔽8), … |
| maximal normal subgroup of | C32×AGL(1,𝔽8), C2×C16×AGL(1,𝔽8), M32×AGL(1,𝔽8), … |
| maximal quotient of | C32×AGL(1,𝔽8), C2×C16×AGL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5506);