Finite Group DatabasebetaFinite Group Databasebeta| order | 14190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D55×C43⋊C3 |
| unambiguous semidirect product | C5⋊(D11×C43⋊C3) |
| unambiguous semidirect product | C11⋊(D5×C43⋊C3) |
| unambiguous semidirect product | (C43×D55)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C43 | C2×C3 |
| LCS | G ▷ C5×C11×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2365 |
493 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×D43⋊C3, D55⋊(D43⋊C3), D5×D11×C43⋊C3, … |
| maximal normal subgroup of | D55×D43⋊C3, D55⋊(D43⋊C3), D5×D11×C43⋊C3, … |
| maximal quotient of | C43⋊C3×Dic55, C2×D55×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14190, 32);