Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C7 ⋊ #1744 |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊#7014, #13240329, #13240351, … |
| maximal normal subgroup of | C7⋊#7014, #13240329, #13240351, … |
| maximal quotient of | #13244219, #13244221, #13244225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1908);