Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#544 ⋊ C2 |
| Sylow | C7 ⋊ #3244 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^6,c^b=ce,d^b=dg,f^c=fg92 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3244, C2×#11740924, #14226046, … |
| maximal normal subgroup of | D7×#3244, C2×#11740924, #14226046, … |
| maximal quotient of | #13363347, #13363569, #13364386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15690);