Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #2298 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C4×C22⋊C4×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C4×C22⋊C4 | D73 |
| hypocenter | C73 | #2298 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
524 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,h^b=h^72,h^c=h^721496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32979462, #32979466, #33084207, … |
| maximal normal subgroup of | #32979462, #32979466, #33084207, … |
| maximal quotient of | #33007102, #33007114, #33007124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7006);