Finite Group DatabasebetaFinite Group Databasebeta| order | 9028 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#6923 |
| Fitting, socle, Hall | C37×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #6923 |
| commutator, hypocenter | C61 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C61 | C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
703 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#6923⋊C3, #41028950, #41028951, … |
| maximal normal subgroup of | C37×#6923⋊C3, #41028950, #41028951, … |
| maximal quotient of | C3×C37×#6923, C37×C3⋊#6923 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9028, 6);