Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C337 ⋊ #126 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^3361694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D337, C2×#24924952, #36341832, … |
| maximal normal subgroup of | #126×D337, C2×#24924952, #36341832, … |
| maximal quotient of | #36341172, #36341187, #36341190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 139);