Finite Group DatabasebetaFinite Group Databasebeta| order | 1932 |
| isoclinism | isoclinic class of D21×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D23 |
| unambiguous semidirect product | (C3×D23)⋊D7 |
| unambiguous semidirect product | (C7×D23)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C23 ⋊ C22 |
| Hall | C7×C23 ⋊ C2×D3 |
| Hall | C3×C23 ⋊ C2×D7 |
| Sylow | C23 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D23 |
| Sylow | C7 ⋊ D3×D23 |
| Sylow | C3 ⋊ D7×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C23 | C22 |
| LCS | G ▷ C3×C7×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 483 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D147, C7×D21×D23, D23×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | C7×D21×D23, D21×AGL(1,𝔽23), C11×D21×D23, … |
| maximal quotient of | D23×D147, C7×D21×D23, D23×C3⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1932, 19);