Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ #1489 |
266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^6,c^b=cf,d^b=df,h^b=h^6158 conjugacy classes — view the full character table.
| maximal subgroup of | #13245843, #13245844, #13245848, … |
| maximal normal subgroup of | #13245843, #13245844, #13245848, … |
| maximal quotient of | #13241952, #13241957, #13241962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2374);