Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×#64408 |
| commutator, socle | C2×C73 | C2×C32 |
| Fitting | C32×C73 | C4 |
| hypercenter | C32 | #64408 |
| hypocenter | C73 | M128 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C16 ◁ C32 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^27,h^b=h^72,h^c=h^72656 conjugacy classes — view the full character table.
| maximal subgroup of | #34001206, #34001207, #34001272, … |
| maximal normal subgroup of | #34001206, #34001207, #34001272, … |
| maximal quotient of | #34001205, #34001211, #34001277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19680);