Finite Group DatabasebetaFinite Group Databasebeta| order | 7353 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#4294 |
| derived, Sylow | C19 ⋊ C9×C43 |
| Hall | C19×C43 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | C19⋊C3 |
| commutator, hypocenter | C19 | C9×C43 |
| Frattini | C3 | C43×C19⋊C3 |
| Fitting, socle | C3×C19×C43 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C43 | |
12 conjugacy classes of subgroups.
1161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#4294, D43×#4294, C43×#4294⋊C2, … |
| maximal normal subgroup of | C2×C43×#4294, D43×#4294, C43×#4294⋊C2, … |
| maximal quotient of | C2×C43×#4294, C43×C22⋊#4294, C5×C43×#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7353, 2);