Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #405×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2957 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D292 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #405×C73 | C2 |
| socle | C2×C73 | C2×C4×D4 |
| hypercenter | #405 | D73 |
| hypocenter | C73 | #2957 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×M16 ◁ #405 | |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^72,e^b=eg,h^b=h^72,d^c=dg1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33002118, #33002122, #33002125, … |
| maximal normal subgroup of | #33002118, #33002122, #33002125, … |
| maximal quotient of | #33055443, #33055451, #33055459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13428);