Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C42×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1284 |
226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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=e,c^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^27,d^b=dg,h^d=h^72608 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624779, #34002372, #34002377, … |
| maximal normal subgroup of | C2×#22624779, #34002372, #34002377, … |
| maximal quotient of | #33999896, #33999904, #33999913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19358);