Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#525 ⋊ C2 |
| Sylow | C7 ⋊ #3002 |
764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | #13248903, #13248905, #13325902, … |
| maximal normal subgroup of | #13248903, #13248905, #13325902, … |
| maximal quotient of | #13325900, #13325951, #13326002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15137);