Finite Group DatabasebetaFinite Group Databasebeta| order | 7548 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C22×C17×C37⋊C3 |
| Fitting, socle, Hall | C22×C17×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C22×C3×C17 |
| Hall | C17×C37 ⋊ C22×C3 |
| Hall | C22×C37 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C17 | C37⋊C3 |
| commutator, hypocenter | C37 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C17×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C17 | |
40 conjugacy classes of subgroups.
1020 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7548, 45);