Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #103×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1866 |
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^46,d^b=dg,e^b=eg,h^b=h^27,d^c=dg,e^c=eg,h^c=h^72,h^f=h^72290 conjugacy classes — view the full character table.
| maximal subgroup of | D73⋊#1866, C2×#22625901, #34021499, … |
| maximal normal subgroup of | D73⋊#1866, C2×#22625901, #34021499, … |
| maximal quotient of | #34005565, #34005568, #34005571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20480);