Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^6,h^b=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1278, C2×#11725473, #13243290, … |
| maximal normal subgroup of | D7×#1278, C2×#11725473, #13243290, … |
| maximal quotient of | #13240323, #13240337, #13240343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 239);