Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #11759818⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11759818⋊C2 |
| Fitting, socle, derived, Sylow | C132 ⋊ C22×C3 |
| Hall | D132 ⋊ C3 |
| Hall | #92789 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2^2,3,13^2|e^a=e^12,d^b=d^12,d^c=d^3,e^c=e^932 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11759818⋊C2, #28382309, #28382310, … |
| maximal normal subgroup of | C7×#11759818⋊C2, C11×#11759818⋊C2, C17×#11759818⋊C2, … |
| maximal quotient of | C7×#11759818⋊C2, #28382309, #28382310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 50);