Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#499 ⋊ C2 |
| Sylow | C7 ⋊ #2242 |
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 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|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,h^a=h^6,h^b=h^6,h^c=h^6104 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2242, C2×#11729105, #13509095, … |
| maximal normal subgroup of | D7×#2242, C2×#11729105, #13509095, … |
| maximal quotient of | #13270178, #13271711, #13271718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3871);