Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×C4⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #2988 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^6188 conjugacy classes — view the full character table.
| maximal subgroup of | #13247678, #13247682, #13247685, … |
| maximal normal subgroup of | #13247678, #13247682, #13247685, … |
| maximal quotient of | #13352584, #13352586, #13352678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11224);