Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#427 ⋊ C2 |
| Sylow | C7 ⋊ C4×#135 |
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^6,h^c=h^6140 conjugacy classes — view the full character table.
| maximal subgroup of | #13269019, #13269024, #13269043, … |
| maximal normal subgroup of | #13269019, #13269024, #13269043, … |
| maximal quotient of | #13323173, #13323325, #13323544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11376);