Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D39⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D13 |
| Fitting, socle, derived, Hall | C3×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×D3 |
| Sylow | C3 ⋊ D132 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C132 | C22 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2^2,3,13^2|c^a=c^2,d^a=d^12,d^b=d^12,e^b=e^12150 conjugacy classes — view the full character table.
| maximal subgroup of | ((C13⋊D13)⋊C7)⋊D3, C7×D39⋊D13, #28382488, … |
| maximal normal subgroup of | C7×D39⋊D13, C11×D39⋊D13, C17×D39⋊D13, … |
| maximal quotient of | C7×D39⋊D13, #28382488, D39⋊D91, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 76);