Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^6230 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2217, C2×#11729168, #13508233, … |
| maximal normal subgroup of | D7×#2217, C2×#11729168, #13508233, … |
| maximal quotient of | #13268012, #13268063, #13268131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3934);