Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C7×C82 ⋊ C2 |
| Sylow | C7 ⋊ #1450 |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,d^2=f,e^2=g,c^b=cf,h^c=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | #13262776, #13262779, #13262784, … |
| maximal normal subgroup of | #13262776, #13262779, #13262784, … |
| maximal quotient of | #13243151, #13243180, #13244224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 567);