Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#450 ⋊ C2 |
| Sylow | C7 ⋊ #3200 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^6,f^c=fg83 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3200, C2×#11737600, #14224517, … |
| maximal normal subgroup of | D7×#3200, C2×#11737600, #14224517, … |
| maximal quotient of | #13362891, #13362905, #13364100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12366);