Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #2836 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | #399×C73 | C2 |
| hypercenter | #399 | D73 |
| hypocenter | C73 | #2836 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #399 | |
358 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^72,c^b=cg,d^b=def,d^c=de818 conjugacy classes — view the full character table.
| maximal subgroup of | #2836×D73, C2×#22618130, #33292274, … |
| maximal normal subgroup of | #2836×D73, C2×#22618130, #33292274, … |
| maximal quotient of | #33016699, #33016735, #33016756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 12709);