Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C73 ⋊ #1420 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17989499 |
| commutator | C16×C73 | C2×C4 |
| Frattini | C16 | C2×#64408 |
| Fitting | Q32×C73 | C4 |
| socle | C2×C73 | #357 |
| hypercenter | Q32 | #64408 |
| hypocenter | C73 | #1420 |
| LCS | G ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^27,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^d=h^72224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22625087, D73⋊#1420, #34014469, … |
| maximal normal subgroup of | C2×#22625087, D73⋊#1420, #34014469, … |
| maximal quotient of | #34000877, #34000878, #34000961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19666);