Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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,h^c=h^6200 conjugacy classes — view the full character table.
| maximal subgroup of | #13241732, #13241734, #13241740, … |
| maximal normal subgroup of | #13241732, #13241734, #13241740, … |
| maximal quotient of | #13244916, #13244920, #13244929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1122);