Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #106×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1776 |
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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=de,d^2=g,e^2=g,b^a=bd,c^a=cg,h^a=h^46,d^b=dg,e^b=eg,h^b=h^46,h^c=h^27,h^e=h^72,h^f=h^72296 conjugacy classes — view the full character table.
| maximal subgroup of | #34012612, #34012738, C2×#22625747, … |
| maximal normal subgroup of | #34012612, #34012738, C2×#22625747, … |
| maximal quotient of | #34003989, #34003993, #34004001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20326);