Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #2097 |
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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=deg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,h^b=h^72,d^c=dg,e^c=eg,h^c=h^721472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2097×D73, C2×#22611478, #33115777, … |
| maximal normal subgroup of | #2097×D73, C2×#22611478, #33115777, … |
| maximal quotient of | #32990981, #32991010, #32991042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6057);