Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#322 ⋊ C2 |
| Sylow | C7 ⋊ #1722 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^6,c^b=cf146 conjugacy classes — view the full character table.
| maximal subgroup of | #13267216, D7×#1722, C2×#11725852, … |
| maximal normal subgroup of | #13267216, D7×#1722, C2×#11725852, … |
| maximal quotient of | #13247585, #13253596, #13253603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 618);