Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C337 ⋊ #131 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,d^2=e,f^a=f^148,c^b=ce,f^b=f^336,f^c=f^336,f^d=f^336440 conjugacy classes — view the full character table.
| maximal subgroup of | #36342348, #36342349, #36342350, … |
| maximal normal subgroup of | #36342348, #36342349, #36342350, … |
| maximal quotient of | #36342270, #36342280, #36342312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 234);