Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×M64 ⋊ C2 |
| Sylow | C7 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^6,c^b=cg,d^b=dg,h^b=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1401, C2×#11725409, #13274005, … |
| maximal normal subgroup of | D7×#1401, C2×#11725409, #13274005, … |
| maximal quotient of | #13241136, #13241196, #13241233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 175);