Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #332×C73 ⋊ C2 |
| Sylow | C73 ⋊ #1691 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556564 |
| commutator | C42×C73 | C23 |
| Frattini | C42 | C22×D73 |
| Fitting | #332×C73 | C2 |
| socle | C22×C73 | #121 |
| hypercenter | #332 | D73 |
| hypocenter | C73 | #1691 |
| LCS | G ▷ C42×C73 ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #332 | |
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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=d,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^72,e^c=eg,h^c=h^72707 conjugacy classes — view the full character table.
| maximal subgroup of | #1691×D73, C2×#22609429, #33068524, … |
| maximal normal subgroup of | #1691×D73, C2×#22609429, #33068524, … |
| maximal quotient of | #32979067, #32982180, #32982190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4008);