Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #3585 |
1464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^c=h^6107 conjugacy classes — view the full character table.
| maximal subgroup of | #13385083, #13385085, #13385105, … |
| maximal normal subgroup of | #13385083, #13385085, #13385105, … |
| maximal quotient of | #14217364, #14217376, #14217477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19026);