Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #472×D73 |
| Fitting | #472×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#472 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #472×C73 | C2 |
| socle | C2×C73 | C2×#121 |
| hypercenter | #472 | D73 |
| hypocenter | C73 | C2×#472 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
488 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #2192×D73, #2193×D73, #33239964, … |
| maximal normal subgroup of | #2192×D73, #2193×D73, #33239964, … |
| maximal quotient of | #1667×D73, #1675×D73, #1677×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 14213);