Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D4×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1460 |
312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=e,c^2=fg,e^2=g,b^a=bd,d^a=df,h^a=h^10,e^b=ef,h^c=h^46,h^e=h^27,h^g=h^72134 conjugacy classes — view the full character table.
| maximal subgroup of | #34032976, #100×#10596842, #34033308, … |
| maximal normal subgroup of | #34032976, #100×#10596842, #34033308, … |
| maximal quotient of | #34033178, #34033180, #34033182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21624);