Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1508 |
294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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=e,b^2=f,c^2=g,d^2=g,b^a=bd,d^a=df,h^a=h^27,c^b=cf,d^b=dg,e^b=efg,h^c=h^72,h^e=h^72392 conjugacy classes — view the full character table.
| maximal subgroup of | #34004270, #34004271, #34004274, … |
| maximal normal subgroup of | #34004270, #34004271, #34004274, … |
| maximal quotient of | #34001347, #34001356, #34001384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19909);