Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D39 |
| unambiguous semidirect product | (C2×C3)⋊(C13×D13) |
| unambiguous semidirect product | (C2×C13)⋊(D3×C13) |
| Fitting, socle | C2×C3×C132 ⋊ C2 |
| derived | C3×C13 ⋊ C22×C13 |
| Hall | C3×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C132 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊#14556975, C13×D7×D39, C2×C13×D273, … |
| maximal normal subgroup of | C2×C7×C13×D39, C2×C11×C13×D39, C2×C13×C17×D39, … |
| maximal quotient of | C13×D7×D39, C2×C13×D273, C2×C7×C13×D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 87);