Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #117×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1826 |
306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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=f,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^27,h^b=h^72,e^c=eg,h^f=h^72398 conjugacy classes — view the full character table.
| maximal subgroup of | #34004540, #34004541, #34004542, … |
| maximal normal subgroup of | #34004540, #34004541, #34004542, … |
| maximal quotient of | #34005200, #34005203, #34005204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20418);