Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1648 |
194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1648, C2×#11729129, #13329632, … |
| maximal normal subgroup of | D7×#1648, C2×#11729129, #13329632, … |
| maximal quotient of | #13242713, #13242720, #13242797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3895);