Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2254 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^6230 conjugacy classes — view the full character table.
| maximal subgroup of | #13241455, #13241457, #13267760, … |
| maximal normal subgroup of | #13241455, #13241457, #13267760, … |
| maximal quotient of | #13270233, #13271831, #13272397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1566);