Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C337 ⋊ #103 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^336,c^b=ce1694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D337, C2×#24924883, #36341300, … |
| maximal normal subgroup of | #103×D337, C2×#24924883, #36341300, … |
| maximal quotient of | Q8⋊#14582106, #36341042, #36341051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 70);