Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#494 ⋊ C2 |
| Sylow | C7 ⋊ #2248 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^6,h^b=h^6104 conjugacy classes — view the full character table.
| maximal subgroup of | #13267234, #13267235, #13267241, … |
| maximal normal subgroup of | #13267234, #13267235, #13267241, … |
| maximal quotient of | #13268461, #13268483, #13268485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3833);