Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13242581, #13242582, #13242591, … |
| maximal normal subgroup of | #13242581, #13242582, #13242591, … |
| maximal quotient of | #13256763, #13256773, #13256803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4312);