Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2100 |
214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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=d,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ceg,c^b=cf,f^b=fg,h^b=h^6,f^c=fg,h^c=h^6152 conjugacy classes — view the full character table.
| maximal subgroup of | #13243060, #13243061, #13243066, … |
| maximal normal subgroup of | #13243060, #13243061, #13243066, … |
| maximal quotient of | #13258927, #13261707, #13262055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1163);