Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C337 ⋊ M32 |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^85,f^b=f^336,f^c=f^148,f^d=f^336188 conjugacy classes — view the full character table.
| maximal subgroup of | #36342405, #36342406, #36342409, … |
| maximal normal subgroup of | #36342405, #36342406, #36342409, … |
| maximal quotient of | #36342399, #36342402, C4⋊#19129197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 243);