Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3324 |
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 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=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,f^c=fg104 conjugacy classes — view the full character table.
| maximal subgroup of | #13343409, #13343411, #13343469, … |
| maximal normal subgroup of | #13343409, #13343411, #13343469, … |
| maximal quotient of | #13369411, #13370261, #13371051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15697);