Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #1416 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=g,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^6,c^b=ce,e^b=ef,f^b=fg104 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1416, C2×#11725632, #13274229, … |
| maximal normal subgroup of | D7×#1416, C2×#11725632, #13274229, … |
| maximal quotient of | #13241249, #13241354, #13241432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 398);