Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×C8×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #2986 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^6,c^b=ceg,d^b=dg,h^d=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13324971, #13324974, #13325008, … |
| maximal normal subgroup of | #13324971, #13324974, #13325008, … |
| maximal quotient of | #13352554, #13352561, #13352848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12134);