Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C16×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#10596842 |
| commutator | C4×C73 | C4×C8 |
| Frattini | C8 | C2×#10596842 |
| Fitting | C16×C73 | C8 |
| socle | C2×C73 | #322 |
| hypercenter | C16 | #10596842 |
| hypocenter | C73 | #1313 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C16 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^51,h^d=h^46,h^f=h^72188 conjugacy classes — view the full character table.
| maximal subgroup of | #34033009, #34033010, C2×#22626951, … |
| maximal normal subgroup of | #34033009, #34033010, C2×#22626951, … |
| maximal quotient of | #34032753, #34032754, #34032857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21530);