Finite Group DatabasebetaFinite Group Databasebeta| order | 1012 |
| isoclinism | isoclinic class of D11×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D23 |
| unambiguous semidirect product | (D11×C23)⋊C2 |
| unambiguous semidirect product | (C11×D23)⋊C2 |
| unambiguous semidirect product | D253⋊C2 |
| Fitting, socle, derived, Hall | C11×C23 ⋊ C22 |
| Sylow | C23 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C23 | C22 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 253 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×D23, D23×D33, D11×D69, … |
| maximal normal subgroup of | C3×D11×D23, D11×AGL(1,𝔽23), C11×D11×D23, … |
| maximal quotient of | C3×D11×D23, D23×D33, D11×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1012, 9);