Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of C13⋊C3×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#261 |
| Fitting, socle, derived, Sylow | C132 ⋊ C3×C4 |
| Hall | C13×#261 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132 | C3×C4 |
| prime radical | D13×C13⋊C3 | C2 |
| cosocle | C13×D13 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 | |
25 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 156 |
49 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C13⋊C3×#261, #28382328, #28382329, … |
| maximal normal subgroup of | C7×C13⋊C3×#261, C11×C13⋊C3×#261, C17×C13⋊C3×#261, … |
| maximal quotient of | C7×C13⋊C3×#261, #28382328, #28382329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 53);