Finite Group DatabasebetaFinite Group Databasebeta| order | 38628 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C29⋊(#66526⋊C2) |
| unambiguous semidirect product | (C2×C29)⋊(#66526⋊C2) |
| unambiguous semidirect product | (C2×#66526)⋊D29 |
| Fitting, socle | C2×C29×C37 ⋊ C2×C9 |
| derived, Hall | C29×C37 ⋊ C22×C9 |
| Hall | C29×#66526 ⋊ C22 |
| Hall | C2×D1073 ⋊ C9 |
| Hall | #66526 ⋊ C2×D29 |
| Sylow | C37 ⋊ C2×C9×D29 |
| Sylow | C29 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C29⋊(#66526⋊C2) |
| commutator, hypocenter | C29×C37 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C37 | C2×C9 |
| prime radical | C2×C29⋊(D37⋊C3) | C3 |
| cosocle | C29×C37⋊C3 | C22×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2146 |
404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38628, 86);