Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #1365 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,c^b=cf,d^b=def,f^b=fg,h^b=h^6149 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1365, C2×#11725371, #13265080, … |
| maximal normal subgroup of | D7×#1365, C2×#11725371, #13265080, … |
| maximal quotient of | #13240586, #13240982, #13241455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 137);