Finite Group DatabasebetaFinite Group Databasebeta| order | 36924 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17×C181 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C17×C181 |
| unambiguous semidirect product | C3⋊(C22×C17×C181) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C17×C181) |
| Fitting, socle | C2×C3×C17×C181 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C17×C181 |
| Hall | C3×C17×C181 ⋊ C22 |
| Hall | C3×C181 ⋊ C22×C17 |
| Hall | C3×C17 ⋊ C22×C181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17×C181 | D3 |
| commutator, cosocle, hypocenter | C3 | C22×C17×C181 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C17×C181 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C17×C181 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18462 |
18462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36924, 49);