Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1384 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^6,d^b=dg152 conjugacy classes — view the full character table.
| maximal subgroup of | #13241363, #13241364, #13241366, … |
| maximal normal subgroup of | #13241363, #13241364, #13241366, … |
| maximal quotient of | #13240672, #13240720, #13240836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 390);