Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #1439 |
780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=d,b^a=bd,c^a=ce,c^b=cf,h^c=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | #13245598, #13245608, #13245625, … |
| maximal normal subgroup of | #13245598, #13245608, #13245625, … |
| maximal quotient of | #13241717, #13241721, #13241723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4090);