Finite Group DatabasebetaFinite Group Databasebeta| order | 1254 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D33 |
| unambiguous semidirect product | C3⋊(C19×D11) |
| unambiguous semidirect product | C11⋊(D3×C19) |
| Fitting, socle, Hall | C3×C11×C19 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C19 |
| Hall | C11×C19 ⋊ D3 |
| Hall | C3×C19 ⋊ D11 |
| Sylow | C11 ⋊ D3×C19 |
| Sylow | C3 ⋊ C19×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C19 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 627 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22)(23,24,25,26,27,28,29,30,31,32,33);(21,22)(24,33)(25,32)(26,31)(27,30)(28,29)342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D33, D3×C19×D11, D33⋊D19, … |
| maximal normal subgroup of | D19×D33, D3×C19×D11, D33⋊D19, … |
| maximal quotient of | C19×Dic33, C2×C19×D33, C19×D99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1254, 10);