Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C337 ⋊ C2 |
| Sylow | C337 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,d^2=e,b^a=bc,f^b=f^3362708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D337, C2×#24924871, #36341267, … |
| maximal normal subgroup of | C22⋊C8×D337, C2×#24924871, #36341267, … |
| maximal quotient of | #36341028, #36341030, #36341032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 58);