Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1379 |
136 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 81 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=g,d^2=f,f^2=g,b^a=bc,h^a=h^6,c^b=cg,d^b=dg176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1379, C2×#11725477, #13268667, … |
| maximal normal subgroup of | D7×#1379, C2×#11725477, #13268667, … |
| maximal quotient of | #13240635, #13240642, #13240649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 243);