Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2070 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=de,c^2=g,d^2=g,b^a=bde,c^a=ce,e^a=eg,f^a=fg,h^a=h^6,c^b=cf,f^b=fg,h^b=h^6,d^c=dg,h^c=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2070, C2×#11726477, #13382519, … |
| maximal normal subgroup of | D7×#2070, C2×#11726477, #13382519, … |
| maximal quotient of | #13258433, #13258447, #13258461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1243);