Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C337 ⋊ C4 |
| Sylow | C337 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^a=bc,c^a=ce,f^a=f^148,d^b=de,f^b=f^336,f^d=f^336683 conjugacy classes — view the full character table.
| maximal subgroup of | #36342209, #36342210, #36342211, … |
| maximal normal subgroup of | #36342209, #36342210, #36342211, … |
| maximal quotient of | #36342149, #36342150, #36342157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 205);