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 ⋊ #1759 |
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 125 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,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | #13245650, #13245652, #13245657, … |
| maximal normal subgroup of | #13245650, #13245652, #13245657, … |
| maximal quotient of | #13244398, #13244403, #13244418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4163);