Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #2062 |
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | #13266647, #13266649, #13266654, … |
| maximal normal subgroup of | #13266647, #13266649, #13266654, … |
| maximal quotient of | #13258196, #13258201, #13258206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4415);