Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#499 ⋊ C2 |
| Sylow | C7 ⋊ #2244 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,h^a=h^6,c^b=cg,h^b=h^6,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | #13267444, #13267445, #13267451, … |
| maximal normal subgroup of | #13267444, #13267445, #13267451, … |
| maximal quotient of | #13270181, #13271725, #13272027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3872);