Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #401⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×#401⋊C7 |
| unambiguous semidirect product | (C2×#401)⋊C7 |
| Fitting, Sylow | C2×#401 ⋊ C7 |
| derived | #401 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #401⋊C7 |
| commutator, cosocle, hypocenter | #401 | C2×C7 |
| Frattini | C23 | C2×AGL(1,𝔽8) |
| Fitting | C2×#401 | C7 |
| socle | C24 | AGL(1,𝔽8) |
| LCS | G ▷ #401 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
20 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#401⋊C7, C22×#401⋊C7 |
| maximal normal subgroup of | C4×#401⋊C7, C22×#401⋊C7 |
| maximal quotient of | C4×#401⋊C7, C2×#2104⋊C7, #23847⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5501);