Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ #1398 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#10596842 |
| commutator | C4×C73 | C4×C8 |
| Frattini | C8 | C2×#10596842 |
| Fitting | C16×C73 | C8 |
| socle | C2×C73 | #346 |
| hypercenter | C16 | #10596842 |
| hypocenter | C73 | #1398 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C16 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^51,c^b=cg,h^b=h^27,h^c=h^46,h^d=h^72,h^e=h^72188 conjugacy classes — view the full character table.
| maximal subgroup of | #34033007, #34033008, #34033096, … |
| maximal normal subgroup of | #34033007, #34033008, #34033096, … |
| maximal quotient of | #34033000, #34033004, #34033132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21601);