Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #444×D73 |
| Fitting | #444×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D73 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #444×C73 | C2 |
| socle | C2×C73 | C2×C4×D4 |
| hypercenter | #444 | D73 |
| hypocenter | C73 | C2×#444 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #444 | |
464 conjugacy classes of subgroups.
836 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D73, AGL(1,ℤ/16)×D73, #33239429, … |
| maximal normal subgroup of | #2180×D73, AGL(1,ℤ/16)×D73, #33239429, … |
| maximal quotient of | SD16⋊C8×D73, #1579×D73, #1580×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13402);