Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1272 |
166 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 41 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,b^2=f,c^2=f,d^2=g,b^a=bc,c^a=ce,h^a=h^10,c^b=cf,d^b=def,h^d=h^27,h^g=h^72128 conjugacy classes — view the full character table.
| maximal subgroup of | #34033028, #34033076, C2×#22626932, … |
| maximal normal subgroup of | #34033028, #34033076, C2×#22626932, … |
| maximal quotient of | #34032739, #34032841, #34032842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21511);