Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×D4×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1318 |
170 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 27 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=d,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^10,c^b=cg,d^b=deg,d^c=dg,h^d=h^27,h^f=h^72116 conjugacy classes — view the full character table.
| maximal subgroup of | #34033027, #34033075, C2×#22626958, … |
| maximal normal subgroup of | #34033027, #34033075, C2×#22626958, … |
| maximal quotient of | #34032759, #34032760, #34032767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21537);