Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of C43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C43⋊C7 |
| unambiguous semidirect product | (C2×C43)⋊C7 |
| Fitting, Sylow | C2×C43 ⋊ C7 |
| derived | C43 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C2×C7 |
| Frattini | C23 | C2×AGL(1,𝔽8) |
| Fitting | C2×C43 | C7 |
| socle | C24 | AGL(1,𝔽8) |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C43⋊C7, #14690⋊C7, #14691⋊C7, … |
| maximal normal subgroup of | C4×C43⋊C7, #14690⋊C7, #14691⋊C7, … |
| maximal quotient of | C4×C43⋊C7, C22×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5500);