Finite Group DatabasebetaFinite Group Databasebeta| order | 1012 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×C23 |
| unambiguous semidirect product | C11⋊(C22×C23) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C23) |
| Fitting, socle | C2×C11×C23 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C23 |
| Hall | C11×C23 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D11 |
| commutator, cosocle, hypocenter | C11 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C23 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 506 |
322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D11×C23, C2×C23×D33, C2×C3×D11×C23, … |
| maximal normal subgroup of | C2×C3×D11×C23, C2×D11×C23⋊C11, C2×C11×D11×C23, … |
| maximal quotient of | D3×D11×C23, C2×C23×D33, C2×C3×D11×C23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1012, 11);