Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #11759818 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#11759818 |
| Fitting, socle | C2×C132 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C22×C3 |
| Hall | C2×C13×D13 ⋊ C3 |
| Hall | #92789 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11759818 |
| commutator, cosocle, hypocenter | C132 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #28382316, #28382317, D7×#11759818, … |
| maximal normal subgroup of | C2×C7×#11759818, C2×C11×#11759818, C2×C17×#11759818, … |
| maximal quotient of | #28382316, #28382317, D7×#11759818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 60);