Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of C22⋊#92788 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#92788 |
| Fitting, socle, derived, Hall | C22×C132 ⋊ C3 |
| Sylow | C132 ⋊ A4 |
| Sylow | C22 ⋊ #92788 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C132 | C3 |
| LCS | G ▷ C22×C132 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 676 |
Polycyclic presentation:
3,2^2,13^2|b^a=c,c^a=bc,d^a=d^3,e^a=e^3228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 82);