Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #1380 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^6236 conjugacy classes — view the full character table.
| maximal subgroup of | #13241351, #13241352, #13241354, … |
| maximal normal subgroup of | #13241351, #13241352, #13241354, … |
| maximal quotient of | #13240666, #13240711, #13240833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 378);