Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#364 ⋊ C2 |
| Sylow | C7 ⋊ #2153 |
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,h^c=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | #13265310, #13265312, #13265315, … |
| maximal normal subgroup of | #13265310, #13265312, #13265315, … |
| maximal quotient of | #13265342, #13265368, #13265401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1823);