Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#491 ⋊ C2 |
| Sylow | C7 ⋊ #1662 |
196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^668 conjugacy classes — view the full character table.
| maximal subgroup of | #13241641, #13241643, D7×#1662, … |
| maximal normal subgroup of | #13241641, #13241643, D7×#1662, … |
| maximal quotient of | #13242649, #13242698, #13242726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3771);