Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C337 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^3362702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341041, #36341043, #36341456, … |
| maximal normal subgroup of | #36341041, #36341043, #36341456, … |
| maximal quotient of | #36341165, #36341178, #36341189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 125);