Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#354 ⋊ C2 |
| Sylow | C7 ⋊ #1404 |
112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,c^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cg,d^b=de,e^b=eg,f^b=fg,h^b=h^6,d^c=dfg,e^c=eg,e^d=eg56 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1404, C2×#11725348, #13274045, … |
| maximal normal subgroup of | D7×#1404, C2×#11725348, #13274045, … |
| maximal quotient of | #13241157, #13241224, #13241320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 114);