Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14582106 |
| Sylow | C337 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,d^2=e,b^a=bc,f^a=f^3362708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341028, #36341029, #36341030, … |
| maximal normal subgroup of | #36341028, #36341029, #36341030, … |
| maximal quotient of | #36341029, #36341031, D4⋊#14582106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 59);