Finite Group DatabasebetaFinite Group Databasebeta| order | 36244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×D13×D41 |
| unambiguous semidirect product | (D13×C41)⋊(C2×C17) |
| unambiguous semidirect product | (C13×D41)⋊(C2×C17) |
| unambiguous semidirect product | D533⋊(C2×C17) |
| Fitting, socle, Hall | C13×C17×C41 ⋊ C22 |
| derived, Hall | C13×C41 ⋊ C22×C17 |
| Hall | C17×C41 ⋊ C2×D13 |
| Hall | C13×C17 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C17×D13 |
| Sylow | C13 ⋊ C2×C17×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D13×D41 |
| commutator, cosocle, hypocenter | C13×C41 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C41 | C22 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9061 |
2992 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36244, 34);