Finite Group DatabasebetaFinite Group Databasebeta| order | 7353 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#4296 |
| Fitting, socle, Hall | C19×C43 ⋊ C9 |
| derived, Sylow | C19 ⋊ C9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #4296 |
| commutator, hypocenter | C19 | C9×C43 |
| Frattini | C1 | G |
| Fitting, socle | C19×C43 | C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C43 | |
12 conjugacy classes of subgroups.
473 conjugacy classes — view the full character table.
| maximal subgroup of | C43×AGL(1,𝔽19), #4296⋊D43, D43×#4296, … |
| maximal normal subgroup of | C43×AGL(1,𝔽19), #4296⋊D43, D43×#4296, … |
| maximal quotient of | C2×C43×#4296, C43×C22⋊#4296, C5×C43×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7353, 7);