Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #1370 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=ce,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^6248 conjugacy classes — view the full character table.
| maximal subgroup of | #13240445, #13240446, #13240448, … |
| maximal normal subgroup of | #13240445, #13240446, #13240448, … |
| maximal quotient of | #13240536, #13240538, #13240659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12);