Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1996 |
324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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=f,b^2=def,c^2=e,b^a=bd,c^a=ce,d^a=dg,h^a=h^46,d^b=dg,f^b=fg,h^b=h^27,h^f=h^72392 conjugacy classes — view the full character table.
| maximal subgroup of | #34004545, #34004547, #34004548, … |
| maximal normal subgroup of | #34004545, #34004547, #34004548, … |
| maximal quotient of | #34008137, #34008139, #34008143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20700);