Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#451 ⋊ C2 |
| Sylow | C7 ⋊ #3004 |
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^6,e^b=eg,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | #13326196, #13326198, #13326274, … |
| maximal normal subgroup of | #13326196, #13326198, #13326274, … |
| maximal quotient of | #13326174, #13326213, #13326252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12394);