Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#410 ⋊ C2 |
| Sylow | C7 ⋊ #2884 |
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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=g,d^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^6107 conjugacy classes — view the full character table.
| maximal subgroup of | #13271387, #13271389, #13271391, … |
| maximal normal subgroup of | #13271387, #13271389, #13271391, … |
| maximal quotient of | #13319622, #13319624, #13319626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10900);