Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1768 |
260 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 121 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=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^a=cg,h^c=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1768, C2×#11726358, C4×#89611, … |
| maximal normal subgroup of | D7×#1768, C2×#11726358, C4×#89611, … |
| maximal quotient of | #13244939, #13244941, #13244946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1124);