Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2873 |
564 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 373 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|a^2=e,b^2=f,e^2=g,d^a=dg,h^a=h^6,c^b=cg188 conjugacy classes — view the full character table.
| maximal subgroup of | #13251129, #13251132, #13251134, … |
| maximal normal subgroup of | #13251129, #13251132, #13251134, … |
| maximal quotient of | #13319380, #13319404, #13319433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14413);