Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #64408⋊C32 |
| derived, Sylow | C73 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #10596842 |
| commutator, hypocenter | C73 | C4×C32 |
| Frattini | C8 | C2×#10596842 |
| Fitting | C16×C73 | C8 |
| socle | C2×C73 | C4×C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C16 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^10,h^b=h^46,h^c=h^27,h^d=h^72,h^e=h^72272 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#10596842, #34032994, #34033087, … |
| maximal normal subgroup of | C32×#10596842, #34032994, #34033087, … |
| maximal quotient of | #34032993, #34033003, #34033129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21594);