Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M32×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^72,c^b=cg1466 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2220×D73, C2×#22612044, #33240449, … |
| maximal normal subgroup of | #2220×D73, C2×#22612044, #33240449, … |
| maximal quotient of | #33000217, #33000268, #33000336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6623);