Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#525 ⋊ C2 |
| Sylow | C7 ⋊ #3005 |
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13385156, #13385161, #13385193, … |
| maximal normal subgroup of | #13385156, #13385161, #13385193, … |
| maximal quotient of | #13326179, #13326218, #13326257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15139);