Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#504 ⋊ C2 |
| Sylow | C7 ⋊ #2223 |
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=dfg,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^6,e^c=eg146 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2223, C2×#11729209, #13508372, … |
| maximal normal subgroup of | D7×#2223, C2×#11729209, #13508372, … |
| maximal quotient of | #13268012, #13268029, #13268063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3975);