Finite Group DatabasebetaFinite Group Databasebeta| order | 14319 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C3×C43×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C32×C43) |
| unambiguous semidirect product | (C3×C37)⋊(C3×C43) |
| Fitting, socle | C3×C37×C43 ⋊ C3 |
| derived, Sylow | C37 ⋊ C32×C43 |
| Hall | C37×C43 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C32×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C43 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4773 |
1935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C43×D37⋊C3, C3×(C37⋊C3)⋊D43, C3×D43×C37⋊C3, … |
| maximal normal subgroup of | C3×C43×D37⋊C3, C3×(C37⋊C3)⋊D43, C3×D43×C37⋊C3, … |
| maximal quotient of | C2×C3×C43×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14319, 13);