Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#461 ⋊ C2 |
| Sylow | C7 ⋊ #3042 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3042, C2×#11737875, #14220740, … |
| maximal normal subgroup of | D7×#3042, C2×#11737875, #14220740, … |
| maximal quotient of | #13339009, #13339018, #13339027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12641);