Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#451 ⋊ C2 |
| Sylow | C7 ⋊ #3011 |
700 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3011, C2×#11737630, #14220259, … |
| maximal normal subgroup of | D7×#3011, C2×#11737630, #14220259, … |
| maximal quotient of | #13326984, #13326990, #13327072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12396);