Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#364 ⋊ C2 |
| Sylow | C7 ⋊ #1336 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ceg,d^b=dg,e^b=eg,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1336, C2×#11725375, #13263589, … |
| maximal normal subgroup of | D7×#1336, C2×#11725375, #13263589, … |
| maximal quotient of | #13240450, #13240453, #13240456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 141);