Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1988 |
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=deg,c^2=efg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cefg,d^b=dg,e^b=eg,f^b=fg,h^c=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1988, C2×#11726554, #13358308, … |
| maximal normal subgroup of | D7×#1988, C2×#11726554, #13358308, … |
| maximal quotient of | #13253779, #13253797, #13253919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1320);