Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C337 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^148,f^b=f^336,f^d=f^336692 conjugacy classes — view the full character table.
| maximal subgroup of | #36342163, #36342164, #36342165, … |
| maximal normal subgroup of | #36342163, #36342164, #36342165, … |
| maximal quotient of | #36342167, #36342169, #36342171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 213);