Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #529×D73 |
| Fitting | #529×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | #529×C73 | C2 |
| hypercenter | #529 | D73 |
| hypocenter | C73 | C2×#529 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1232 conjugacy classes of subgroups.
1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1482×D73, #1483×D73, #33052534, … |
| maximal normal subgroup of | #1482×D73, #1483×D73, #33052534, … |
| maximal quotient of | #2283×D73, #2290×D73, #2293×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17768);