Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #1346 |
124 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 35 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=g,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cf,d^b=def,h^b=h^6,d^c=dg89 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1346, C2×#11725301, #13263995, … |
| maximal normal subgroup of | D7×#1346, C2×#11725301, #13263995, … |
| maximal quotient of | #13240483, #13240489, #13240507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 67);