Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3329 |
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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=eg,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^72,c^b=cg,d^b=de,h^b=h^72,f^c=fg,h^d=h^721037 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33075706, #33075708, #33075766, … |
| maximal normal subgroup of | #33075706, #33075708, #33075766, … |
| maximal quotient of | #33101627, #33102446, #33103320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 16806);