Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C7×Q32 ⋊ C2 |
| Sylow | C7 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2251, C2×#11729255, #13509217, … |
| maximal normal subgroup of | D7×#2251, C2×#11729255, #13509217, … |
| maximal quotient of | #13268468, #13268470, #13268477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4021);