Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | Aut(G) order 14493696 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5392 |
| Fitting | C16×C337 ⋊ C2 |
| Sylow | C337 ⋊ D16 |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^336,c^b=cd,d^b=de,f^b=f^3362699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341140, D10784, #36341142, … |
| maximal normal subgroup of | #36341140, D10784, #36341142, … |
| maximal quotient of | #36341107, #36341131, D10784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 88);