Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1312 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1312, C2×#11725305, #13262784, … |
| maximal normal subgroup of | D7×#1312, C2×#11725305, #13262784, … |
| maximal quotient of | #13240413, #13240623, #13241128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 71);