Finite Group DatabasebetaFinite Group Databasebeta| order | 10352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D647)⋊C4 |
| Fitting | C2×C4×C647 ⋊ C2 |
| Sylow | C647 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,647|a^2=d,b^a=bc,e^b=e^6462594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D647, C2×(C2×D647)⋊C4, #35208369, … |
| maximal normal subgroup of | C22⋊C4×D647, C2×(C2×D647)⋊C4, #35208369, … |
| maximal quotient of | C647⋊#95, (C2×D647)⋊C8, #35208326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10352, 17);