Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3394 |
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,b^2=eg,c^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^72,d^b=de,f^c=fg,h^c=h^721475 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33075896, #33075903, #33076031, … |
| maximal normal subgroup of | #33075896, #33075903, #33076031, … |
| maximal quotient of | #33102782, #33102800, #33104817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17508);