Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #1323 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^6158 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1323, C2×#11725331, #13262938, … |
| maximal normal subgroup of | D7×#1323, C2×#11725331, #13262938, … |
| maximal quotient of | #13240437, #13240439, #13240441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 97);