Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D13×C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×Dic13 |
| derived, Sylow | C132 ⋊ C3×C4 |
| Hall | C13×Dic13 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D13×C13⋊C3 |
| commutator, hypocenter | C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C132 | C2×C3 |
| prime radical | C2×C13×C13⋊C3 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C13⋊C3×Dic13, #28382185, #28382186, … |
| maximal normal subgroup of | C7×C13⋊C3×Dic13, C11×C13⋊C3×Dic13, C17×C13⋊C3×Dic13, … |
| maximal quotient of | C7×C13⋊C3×Dic13, #28382185, #28382186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 27);