Finite Group DatabasebetaFinite Group Databasebeta| order | 4332 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C19 |
| direct product | D3×C19⋊D19 |
| unambiguous semidirect product | (D3×C19)⋊D19 |
| Fitting, socle, derived, Hall | C3×C192 ⋊ C22 |
| Sylow | C192 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C192 | C22 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1083 |
546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C19⋊D19, D3×#14524206, D3×#14524207, … |
| maximal normal subgroup of | D3×#14524206, D3×#14524207, D3×(C19⋊C3)⋊D19, … |
| maximal quotient of | D9×C19⋊D19, C3×D3×C19⋊D19, C3⋊D3×C19⋊D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4332, 51);