Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^6,h^b=h^6,h^c=h^6140 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1764, C2×#11728043, #13351640, … |
| maximal normal subgroup of | D7×#1764, C2×#11728043, #13351640, … |
| maximal quotient of | #13244470, #13244483, #13244487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2809);