Finite Group DatabasebetaFinite Group Databasebeta| order | 37698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D309 |
| unambiguous semidirect product | C3⋊(C61×D103) |
| unambiguous semidirect product | C103⋊(D3×C61) |
| Fitting, socle, Hall | C3×C61×C103 ⋊ C2 |
| derived, Hall | C3×C103 ⋊ C2×C61 |
| Hall | C61×C103 ⋊ D3 |
| Hall | C3×C61 ⋊ D103 |
| Sylow | C103 ⋊ D3×C61 |
| Sylow | C3 ⋊ C61×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D309 |
| commutator, cosocle, hypocenter | C3×C103 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C61×C103 | C2 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18849 |
9516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37698, 10);