Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1352 |
154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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=d,b^2=eg,c^2=fg,b^a=bc,c^a=ce,e^a=eg,h^a=h^6,c^b=cf,d^b=defg,h^b=h^6,d^c=dg89 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1352, C2×#11725257, #13264073, … |
| maximal normal subgroup of | D7×#1352, C2×#11725257, #13264073, … |
| maximal quotient of | #13240594, #13240615, #13240917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 23);