Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #1441 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D73 |
| commutator | C23×C73 | C22×C4 |
| Fitting | C22×C4⋊C4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C22×C4⋊C4 | D73 |
| hypocenter | C73 | #1441 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=d,c^2=d,b^a=bd,c^a=ce,h^a=h^72,c^b=cf1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32973107, #32973108, #32977790, … |
| maximal normal subgroup of | #32973107, #32973108, #32977790, … |
| maximal quotient of | #32973908, #32973911, #32973912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 2763);