Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 296 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) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,c^2=eg,f^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | #13264162, #13264164, #13264172, … |
| maximal normal subgroup of | #13264162, #13264164, #13264172, … |
| maximal quotient of | #13244301, #13244309, #13244313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1493);