Finite Group DatabasebetaFinite Group Databasebeta| order | 1012 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D23 |
| Fitting, socle | C2×C11×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C22×C11 |
| Hall | C11×C23 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D23 |
| commutator, cosocle, hypocenter | C23 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C23 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 506 |
286 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D23, C2×C11×D69, C2×C3×C11×D23, … |
| maximal normal subgroup of | C2×C3×C11×D23, C2×D23⋊C121, C2×D23×C121, … |
| maximal quotient of | D3×C11×D23, C2×C11×D69, C2×C3×C11×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1012, 10);