Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×#100 ⋊ C2 |
| Sylow | C7 ⋊ #1914 |
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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) = 112 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg,h^c=h^695 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1914, C2×#11727843, #13355827, … |
| maximal normal subgroup of | D7×#1914, C2×#11727843, #13355827, … |
| maximal quotient of | #13249328, #13249338, #13249776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2609);