Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#462 ⋊ C2 |
| Sylow | C7 ⋊ #3328 |
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^6,c^b=cg,d^b=de,h^b=h^6,f^c=fg,h^c=h^6,h^d=h^686 conjugacy classes — view the full character table.
| maximal subgroup of | #13343541, #13343543, #13343601, … |
| maximal normal subgroup of | #13343541, #13343543, #13343601, … |
| maximal quotient of | #13369440, #13370264, #13371065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12706);