Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×#97 ⋊ C2 |
| Sylow | C7 ⋊ #1752 |
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 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,b^2=f,c^2=e,e^2=g,b^a=bd,h^a=h^6,c^b=cg176 conjugacy classes — view the full character table.
| maximal subgroup of | #13268910, #13268912, D7×#1752, … |
| maximal normal subgroup of | #13268910, #13268912, D7×#1752, … |
| maximal quotient of | #13244266, #13244270, #13244293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2351);