Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #11759816 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Sylow | C132 ⋊ C3×C4 |
| Hall | #10621725 ⋊ C3 |
| Hall | #92789 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11759816 |
| commutator, hypocenter | C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C132 | C2×C3 |
| prime radical | C2×#92789 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2,3,13^2,2|a^2=e,c^a=c^12,d^a=d^12,c^b=c^3,d^b=d^968 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523129, #28382175, #28382193, … |
| maximal normal subgroup of | C7×#14523129, C11×#14523129, C17×#14523129, … |
| maximal quotient of | C7×#14523129, #28382175, #28382193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 23);