Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C337 ⋊ C4 |
| Sylow | C337 ⋊ #97 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^148,f^d=f^336692 conjugacy classes — view the full character table.
| maximal subgroup of | #36342195, #36342196, C2×#24925013, … |
| maximal normal subgroup of | #36342195, #36342196, C2×#24925013, … |
| maximal quotient of | #36342146, #36342147, #36342170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 200);