Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C337 ⋊ C2 |
| Sylow | C337 ⋊ #102 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^336,c^b=ce,f^b=f^3362702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D337, C2×#24924881, #36341300, … |
| maximal normal subgroup of | #102×D337, C2×#24924881, #36341300, … |
| maximal quotient of | #36341034, #36341040, #36341048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 68);