Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1317 |
150 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 37 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=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,d^b=de,h^b=h^6,d^c=dg92 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1317, C2×#11725251, #13262879, … |
| maximal normal subgroup of | D7×#1317, C2×#11725251, #13262879, … |
| maximal quotient of | #13240416, #13240424, #13240543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17);