Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #2170 |
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 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|a^2=e,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^63,d^b=dg,h^c=h^10,h^e=h^27,h^f=h^72119 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22627149, #34034832, #34034838, … |
| maximal normal subgroup of | C2×#22627149, #34034832, #34034838, … |
| maximal quotient of | #34033935, #34033941, SD16×#11924040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21728);