Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C7⋊#1308 |
| Sylow | C7 ⋊ #1308 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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,d^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^6,c^b=cg,d^b=df110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1308, C2×C7⋊#1308, #13244198, … |
| maximal normal subgroup of | D7×#1308, C2×C7⋊#1308, #13244198, … |
| maximal quotient of | #13240368, #13240369, #13240370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 331);