Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ #2951 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^6,e^b=eg,h^b=h^6,d^c=dg,h^d=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | #13507133, #13507137, #13507144, … |
| maximal normal subgroup of | #13507133, #13507137, #13507144, … |
| maximal quotient of | #13323277, #13323504, #13323648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11932);