Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#339 ⋊ C2 |
| Sylow | C7 ⋊ #1826 |
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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=f,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^6,e^c=eg122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1826, C2×#11726508, #13353625, … |
| maximal normal subgroup of | D7×#1826, C2×#11726508, #13353625, … |
| maximal quotient of | #13247142, #13247146, #13247150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1274);