Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C337 ⋊ #108 |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^148,f^b=f^336,f^d=f^336686 conjugacy classes — view the full character table.
| maximal subgroup of | #36342219, #36342220, #36342233, … |
| maximal normal subgroup of | #36342219, #36342220, #36342233, … |
| maximal quotient of | #36342167, #36342168, #36342181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 217);