Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #2089 |
176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,b^2=d,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^6,c^b=cf,f^b=fg,e^c=eg,f^c=fg92 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2089, C2×#11728424, #13382919, … |
| maximal normal subgroup of | D7×#2089, C2×#11728424, #13382919, … |
| maximal quotient of | #13258705, #13258710, #13258715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3190);